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
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
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.