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Answer:
The length of the mat is 30 inches.
Step-by-step explanation:
Let H be the hypotenuse of the incline mat, L its length and h its height.
It is given that H = L + 4 and h = L - 14. Now, using Pythagoras' theorem for right-angled triangles, H² = L² + h²
(L + 4)² = L² + (L - 14)²
Expanding, we have
L² + 8L + 16 = L² + L² -28L + 196
collecting all the terms to the right side, we have
L² + L² -28L + 196 - L² - 8L - 16 = 0
L² - 36L + 180 = 0
Using the quadratic formula, L =
L
We use the larger answer L = 30 inches since L = 6 would give h = L -14 = 6 - 14 = -8 .
So, the length of the mat is 30 inches.