The ratio of corresponding sides of two similar triangles is 2:7. The sides of the smaller triangle are 16 centimeters, 22 centimeters and 28 centimeters long. What is the perimeter of the larger triangle?
the perimeters are also in the ratio of 2:7
So, find the perimeter of the smaller triangle, and multiply it by 7/2
To find the perimeter of the larger triangle, we can use the fact that corresponding sides of similar triangles are proportional.
Let's call the sides of the larger triangle A, B, and C. The corresponding sides of the smaller triangle are 16, 22, and 28 centimeters long. So, we can set up the proportion:
A/16 = B/22 = C/28 = 2/7
To find the value of A, we can solve the proportion:
A/16 = 2/7
Cross-multiplying, we get:
7A = 2 * 16
7A = 32
A = 32/7
Similarly, for B and C:
B/22 = 2/7
7B = 2 * 22
7B = 44
B = 44/7
C/28 = 2/7
7C = 2 * 28
7C = 56
C = 56/7
Now we have the lengths of the corresponding sides of the larger triangle:
A = 32/7 cm
B = 44/7 cm
C = 56/7 cm
To find the perimeter, we add up the lengths of the sides:
Perimeter = A + B + C
= (32/7) + (44/7) + (56/7)
= (32 + 44 + 56)/7
= 132/7
= 18.8571 cm (rounded to four decimal places)
Therefore, the perimeter of the larger triangle is approximately 18.8571 centimeters.
To find the perimeter of the larger triangle, we need to determine the lengths of its corresponding sides.
Given that the ratio of corresponding sides of two similar triangles is 2:7, we can set up the proportion:
2/7 = length of corresponding side in smaller triangle / length of corresponding side in larger triangle
Let's label the sides of the smaller triangle as a, b, and c, and the corresponding sides of the larger triangle as x, y, and z.
So, we have:
2/7 = a/x
2/7 = b/y
2/7 = c/z
We are given the lengths of the sides of the smaller triangle as 16 cm, 22 cm, and 28 cm. Let's substitute these values into the equation and solve for the corresponding sides of the larger triangle.
Using the first equation, we have:
2/7 = 16/x
Cross-multiplying:
2x = 16 * 7
2x = 112
x = 112/2
x = 56
Similarly, using the second equation, we have:
2/7 = 22/y
2y = 7 * 22
2y = 154
y = 154/2
y = 77
And using the third equation, we have:
2/7 = 28/z
2z = 7 * 28
2z = 196
z = 196/2
z = 98
Now that we have the lengths of the corresponding sides of the larger triangle, we can find the perimeter by adding them together:
Perimeter = x + y + z
Perimeter = 56 + 77 + 98
Perimeter = 231 centimeters
Therefore, the perimeter of the larger triangle is 231 centimeters.