Question

Two right triangular gardens each have a shorter leg 20 feet. The length of the longer leg of one garden is twice the length of the longer leg of the other garden. The perimeter of the larger garden is 1.6 times the perimeter of the other garden. What is the approximate length of the longer leg of the smaller garden? Use a graphing calculator to help you determine the answer.

Answer 1

about 24.38 feet

Explanation:

Graphing window: [0, 30] by [-20, 160]

y1 = 20 + 2x + √(400 + 4x^2)

y2 = 1.6(20 + x + √(400 + x^2))

y1 = y2 when x = 24.3798.

So the length of the smaller garden's longer leg is about 24.38 feet.