Question

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 length of the shorter leg is__________.

PLZ HURRY.

Answer 1

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.