in two congruent triangles the ratio of lengths of two corresponding sides is 5:8. If the perimeter of the larger triangle is 10 ft less than twice the perimeter of the smaller triangle find the perimeter of each triangle

Question

in two congruent triangles the ratio of lengths of two corresponding sides is 5:8. If the perimeter of the larger triangle is 10 ft less than twice the perimeter of the smaller triangle find the perimeter of each triangle

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2 answers
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Answer 1

John1 answered
7 years ago

5/8 = x/(2x-10)

x = perimeter of smaller
2x - 10 = perimeter of larger

8x = 10x -50

-2x = -50 x = 25 smaller

2x-10 2(25)-10 = 50 -10 or 40 for larger

Answer 2

Explain Bot answered
11 months ago

To find the perimeters of the congruent triangles, let's assume the lengths of the corresponding sides in one of the triangles are 5x and 8x, where x is a positive number.

Perimeter of the smaller triangle = sum of all its side lengths = 5x + 8x + 5x = 18x.

Perimeter of the larger triangle = 2 * (perimeter of the smaller triangle) - 10
= 2 * (18x) - 10
= 36x - 10.

Since both triangles are congruent, they have the same perimeter. Therefore, we can set the expressions for their perimeters equal to each other:

18x = 36x - 10.

To solve this equation, let's isolate x:

18x - 36x = -10,
-18x = -10,
x = -10 / -18,
x = 5 / 9.

Now that we have the value of x, we can substitute it back into the expressions for the perimeter of each triangle to find their values:

Perimeter of the smaller triangle = 18x = 18 * (5/9) = 90/9 = 10 ft.

Perimeter of the larger triangle = 36x - 10 = 36 * (5/9) - 10 = 180/9 - 90/9 = 90/9 = 10 ft.

Therefore, the perimeter of each triangle is 10 ft.