Find the length of the shorter leg of a right triangle if the longer leg is 14 feet more than the shorter leg and the hypotenuse is 14 feet less than twice the shorter leg. The …

Question

asked Jun 12, 2019 133k views

1 Answer

Dan Healy · Answer 1 · 2019-06-19T07:50:02+0000

Answer: 42 feet.

Explanation:

Let's call the shorter side: x

Based on the information given in the problem, you know that:

Longer side:
x+14

Hypotenuse:
2x-14

- Apply the Pythagorean Theorem:

a^2=b^2+c^2

Where a is the hypotenuse and b and c are the legs.

- Substitute values. Therefore, you obtain:

(2x-14)^2=x^2+(x+14)^2

- Solve for x. Keep on mind that:

$(a+b)^2=a^2+2ab+b^2\\\\(a-b)^2=a^2-2ab+b^2$

Then:

$(2x)^2-2(2x)(14)+14^2=x^2+x^2+2(x)(14)+14^2\\\\4x^2-56x+196=2x^2+28x+196\\\\2x^2-84x=0\\\\2x(x-42)=0\\\\x_1=0\\x_2=42$

Therefore, the length of the shorter leg is 42 feet.