show that (4,5,3), (1,7,4),and(2,4,6) are vertices of an equilateral triangle
1. show that (4,5,3), (1,7,4),and(2,4,6) are vertices of an equilateral triangle
Vektor (4, 5, 3), (1, 7, 4), dan (2, 4, 6) merupakan vektor dari segitiga sama sisi. Karena ketiga sisi segitiga tersebut sama besar yakni √14. Nilai tersebut diperoleh dari perhitungan panjang vektor pada segitiga. Simak pembahasan berikut.
PembahasanDiketahui:
A = (4, 5, 3)
B = (1, 7, 4)
C = (2, 4, 6)
Ditanya: apakah segitiga ABC merupakan segitiga sama sisi
Jawab:
Syarat segitiga ABC merupakan segitiga sama sisi adalah memiliki panjang sisi yang sama atau dapat ditulis sebagai berikut:
a = b = c
dengan:
a = panjang vektor BC atau |BC|
b = panjang vektor AC atau |AC|
c = panjang vektor AB atau |AB|
Menghitung panjang sisi a
a = panjang vektor BC atau |BC|, maka menghitung vektor BC terlebih dahulu.
vektor BC = C - B
vektor BC = (2, 4, 6) - (1, 7, 4)
vektor BC = (2 - 1, 4 - 7, 6 - 4)
vektor BC = (1, -3, 2)
Panjang vektor BC adalah:
|BC| = [tex]\sqrt{1^{2}+(-3)^{2}+2^{2}}[/tex]
|BC| = [tex]\sqrt{1+9+4}[/tex]
|BC| = √14
∴jadi panjang sisi a adalah √14.
Menghitung panjang sisi b
b = panjang vektor AC atau |AC|, maka menghitung vektor AC terlebih dahulu.
vektor AC = C - A
vektor AC = (2, 4, 6) - (4, 5, 3)
vektor AC = (2 - 4, 4 - 5, 6 - 3)
vektor AC = (-2, -1, 3)
Panjang vektor AC adalah:
|AC| = [tex]\sqrt{(-2)^{2}+(-1)^{2}+3^{2}}[/tex]
|AC| = [tex]\sqrt{4+1+9}[/tex]
|AC| = √14
∴jadi panjang sisi b adalah √14.
Menghitung panjang sisi c
c = panjang vektor AB atau |AB|, maka menghitung vektor AB terlebih dahulu.
vektor AB = B - A
vektor AB = (1, 7, 4) - (4, 5, 3)
vektor AB = (1 - 4, 7 - 5, 4 - 3)
vektor AB = (-3, 2, 1)
Panjang vektor AB adalah:
|AB| = [tex]\sqrt{(-3)^{2}+2^{2}+1^{2}}[/tex]
|AB| = [tex]\sqrt{9+4+1}[/tex]
|AB| = √14
∴jadi panjang sisi c adalah √14.
Karena panjang a = panjang b = panjang c = √14, maka terbukti bahwa segitiga ABC merupakan segitiga sama sisi.
Pelajari lebih lanjutMenghitung proyeksi ortogonal vektor https://brainly.co.id/tugas/22666878Menentukan vektor pada segitiga https://brainly.co.id/tugas/22653997----------------------------------------Detil jawabanKelas: 10
Mapel: Matematika
Bab: Vektor
Kode: 10.6.2
Kata kunci: vektor, segitiga sama sisi, a, b, c, sama panjang
2. The diagram shows triangle abc with vertices a(1, 1) b(1, 3) and c(5, 5) .a.find the area of triangle abcb.find the gradient of the line passing through b and cc.find the equation of the line passing through a and c
Jawaban:
jawaban ada pada lampiran tersebut
Penjelasan dengan langkah-langkah:
untuk 6a bikin imaginary line supaya ada straight line sebagai tingginya
3. the measures of three sides of a triangle are 9,16,20. determine whether the triangle is a right triangle. explain your answer..
i dont know what you say
4. the length of 3 sides of a triangle are in the ratio 5 : 4 :7.the longest side measures 77 cm.the length of the shortest side of the triangle is...cm
Jawaban:
44 cm
Penjelasan dengan langkah-langkah:
panjang terpendek adalah
4/7 x 77
=4 x 11
= 44
5. The sides of a triangle are (2x + 1) cm,(3x + 2) cm and (4x - 1) cm.2x+13x + 24x-1(a) Find the perimeter of the triangle interms of x.(b) If the perimeter of the triangle is 47 cm,find the value of x.
Jawab:
a. 9x cm
b. 5,2 cm
Penjelasan dengan langkah-langkah:
What is known :
side 1 = (2x+1) cm
side 2 = (3x+2) cm
side 3 = (4x-3) cm
a. Perimeter in terms of x
P = s1 + s2 + s3
= 2x + 1 + 3x +2 + 4x - 3
= 9x cm
b. Value of the x if the perimeter is 47 cm
P = s1 + s2 + s3
47 = 9x
x = 5,2 cm
Sorry If I'm wrong, hope it helps
6. There are types of triangles based on the side.....except: A. Obtuse Triangle B. Equilateral Triangle C. Isosceles Triangle D. Scalene Triangledibantu iya
Jawaban:
A. Obtuse Triangle (Segitiga Tumpul)
Penjelasan:
A. Obtuse Triangle (Segitiga Tumpul)
B. Equilateral Triangle (Segitiga Sama Sisi)
C. Isosceles Triangle (Segitiga Sama Kaki)
D. Scalene Triangle (Segitiga Sembarang)
Jawabannya yg A karena Segitiga Tumpul termasuk dalam segitiga yg ditinjau dari Sudutnya, sedangkan yg B, C, dan D itu termasuk dalam segitiga
yg ditinjau dari PanjangSisi-sisinya.
Jawaban:
A. Obtuse triangles
Langkah langkah :
Pertanyaan :
There are types of triangles based on the side except :
Artinya :
Ada jenis jenis segitiga berdasarkan sisinya kecuali :
Pilihan jawaban :
A. Obtuse triangle = segitiga
tumpul
B. Equilateral triangle = segitiga
sama sisi
C. Isosceles triangle = segitiga
sama kaki
D. Scalene triangle = segitiga
sembarang
Penjelasan :
Menurut jenis sisinya, segitiga dibagi menjadi 3 jenis
1. Segitiga sama sisi = ketiga sisi
nya sama panjang dan ketiga
sudutnya sama besar
2. Segitiga sama kaki = Hanya
memiliki 2 sisi sama panjang
dan 2 sudut sama besar.
3. Segitiga sembarang =
segitiga yang masing masing
sisinya tidak sama panjang
dan masing masing sudutnya
tidak sama besar.
Sedangkan segitiga sembarang (scalene triangle) merupakan segitiga berdasarkan jenis sudutnya.
Jadi, jawaban yang tepat untuk pertanyaan diatas adalah
= A. Obtuse triangle
Semoga membantu...
Semoga bermanfaat...
7. The length of the sides of a triangle are 48cm, 14cm, and 50cm, it's circum radius is
hypothenuse / 2 = 25cm
8. If the angles of a triangle are inthe ratio 1:3:5, then how many degrees are in the measure of the smalest angle?
Jawab:
Penjelasan dengan langkah-langkah:
Jawaban:
angles ratio = 1 : 3 : 5
= x, 3x, 5x
smallest angle = x
total angles in triangle = 180⁰
x+3x+5x= 180
9x= 180
x= 20⁰---------
semangat belajar...
9. A piece of wire is bent to form a triangle. The sides of the triangle are in the ratio 3:4:5. The length of the longest side is 35cm. Find the length of the wire used to form the triangle.
[tex] \frac{3 + 4 + 5}{5} \times 35 \: cm \\ \\ \frac{12}{5} \times 35 \: cm = 84 \: cm[/tex]
10. The angle of a triangle are (x-35 ) ,(x-25) and (1/2 x-10 ) what is the largest angle of the triangle
sum of angles = 180°
x-35 + x-25 + 0.5x-10 = 180°
2.5x - 70 = 180°
2.5x = 250
x = 100
angle 1 => 100 - 35 = 65°
angle 2 => 100 - 25 = 75°
angle 3 => 50 - 10 = 40°
May it favours you :)
11. 18. If the size of the angles of triangle are 3x°,4x°and 5x°. The biggest angle of triangle is ...
sudut segitiga = 180°
3x° + 4x° + 5x° = 180°
12x = 180
x = 180/12
x = 15
sudut terbesar = 5x = 5 × 15 = 75°
12. The area of a triangle is 528cm2. the length of its base is 33cm. calculate the perpendicular height of the triangle.
Diketahui:
Luas segitiga = 528 cm²
Panjang alas = 33 cm
Tinggi = ?
[tex]luas \: = 528 \\ \frac{1}{2} \times a \times t = 528 \\ \frac{1}{2} \times 33 \times t = 528 \\ t = \frac{528 \times 2}{33} \\ t = 32[/tex]
Jadi, tinggi segitiga adalah 32 cm.
Jawab:
32
Penjelasan dengan langkah-langkah:
L=528
a= 33
L= a*t/2
528= 33*t/2
1056=33t
t= 1056/33
t=32
13. How many edges are there in a graph with 15 vertices each of degree 4?
Jawaban:
️️️️️️
Penjelasan dengan langkah-langkah:
gabisa bhs inggris
14. If the angles of a triangle are inthe ratio 1:3:5, then how many degrees are in the measure of the smalest angle?
Jawaban:
22.5 degrees
Penjelasan:
one triangle has total of 360 degrees
so :
one plus three plus five equals eight
small angle of triangle has a ratio 1 of 8 (1/8)
1/8 . 180 = 22.5 degrees
15. if triangle ABC and triangle DEF are similiar,the value of x + y=.... cm panjang a ke C = 18cm
DE = 5 cm (triple pythagoras)
[tex] \frac{bc}{ef} = \frac{ac}{df} \\ \frac{x}{3} = \frac{18}{4} \\ 4x = 54 \\ x = \frac{54}{4} \\ x = 13.5[/tex]
[tex] \frac{ab}{de} = \frac{ac}{df} \\ \frac{y}{5} = \frac{18}{4} \\ 4y = 90 \\ y = 22.5 [/tex]
jadi x + y = 13,5 + 22,5 = 36,0
semoga membantu
16. Perimeter of a triangle is 217 cm.the ratio of the triangle sides are 5:9:17 find the length of each side of the triangle
Answer :
Known Values :
Perimeter (P) = 217 cm
Ratio of the sides = 5 : 9 : 17
First, find the value of each "1x" in the ratio ;
=> 217 cm : (5 + 9 + 17)
=> 217 cm : 31
=> 7 cm
Now, we can search each length of each side of the triangle according to the value of each "1x" we searched before.
"A" side :
=> 5 × 7 cm
=> 35 cm
"B" side :
=> 9 × 7 cm
=> 63cm
"C" side :
=> 12 × 7 cm
=> 84cm
So, we found the length for each side in the triangle are 35 cm, 63 cm, and 84 cm.
17. 3 Two vertices of a rectangle, ABCD, are A(-6, -4) and B(4, -8). Find the gradient of CD and the gradient of BC.
Two vertices of a rectangle, ABCD, are A(–6, –4) and B(4, –8).
The gradient of CD is –2/5 (or –0.4).The gradient of BC is 5/2 (or 2.5).Penjelasan dengan langkah-langkah:
On rectangle [tex]ABCD[/tex]:
[tex]CD \parallel AB[/tex], and [tex]BC \perp AB[/tex], or [tex]BC\perp CD[/tex].Thus, the gradient of [tex]CD[/tex] equals the gradient of [tex]AB[/tex], and the gradient of [tex]BC[/tex] equals –1/(the gradient of [tex]AB[/tex]) or –1/(the gradient of [tex]CD[/tex])
Solving them:
[tex]\begin{aligned}m_{CD}&=m_{AB}\quad\because CD\parallel AB\\&=\frac{y_B-y_A}{x_B-x_A}\\&=\frac{-8-(-4)}{4-(-6)}\\&=\frac{-4}{10}\\\therefore\ m_{CD}&=\boxed{\,\bf{-}\frac{2}{5}\,}\end{aligned}[/tex]
[tex]\begin{aligned}m_{BC}&=\frac{-1}{m_{AB}}\quad\because BC\perp AB\\&=\frac{-1}{m_{CD}}\quad\because BC\perp CD.\ {\sf too.\ }\\&=\frac{-1}{\left({-}\dfrac{2}{5}\right)}\\&=-1\times\left(-\frac{5}{2}\right)\\\therefore\ m_{BC}&=\boxed{\,\bf\frac{5}{2}\,}\\\end{aligned}[/tex]
[tex]\blacksquare[/tex]
18. The base of a triangle is longer than twice its corresponding height by 1 cm. The area of the triangle is 105 cm?. Find the height of the triangle!butuh cepat
Jawaban:
52,5
Penjelasan dengan langkah-langkah:
105:2 sorry if wrong
Jawab:
The height of the triangle is 10 cm.
Penjelasan dengan langkah-langkah:
If the area, base and height of that triangle are notated by A, b and h, then it is known that:
A = (1/2)bh
b = 2h+1
So:
A = (1/2) × (2h+1) × h
A = (1/2) × (2h²+h)
2A = 2h²+h
2×105 = 2h²+h
210 = 2h²+h
2h²+h-210 = 0
(2h+21)(h−10)=0
2h+21=0 or h−10=0
h = -21/2 or h = 10
The positive solution is h = 10, so the height of the triangle is 10 cm.
Proof:
If the height is 10 cm, then the base equals to 21 cm (2×10 + 1 = 21).
The area of the triangle:
A = (1/2)bh = (1/2)(21)(10) = (1/2)(210) = 105 cm². (correct!)
19. If the size of the angles of triangle are 3x°,4x°,5x°.the smallest angle of the triangle is
Jawaban Master Teacher
12x = 180°
x = 15°
smallest angle
3x = 45°20. 1.what are some possible lengths of each side of the triangle is isosceles?2.what are some possible lengths of each side if the triangle is scalene?tolong jawab ya kakak adik
Jawaban:
1. The triangle is formed by 3 vertices whose positions are not in line connected.
In each triangle, several properties apply, including;
the sum of the lengths of the two sides is always greater than the side lengths of the triangle;
the sum of the angles of a triangle is 180 degrees;
the largest corner is the corner facing the longest side, while the smallest corner is the corner facing the shortest side;
the size of the outer corner is equal to the sum of the two corners that are not aligned with the outer corner.
2. that the sum of the lengths of each of the two sides of the triangle must be greater than or equal to the length of the third side.
Penjelasan dengan langkah-langkah:
I hope this helps
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