Answer: 42 feet.
Step-by-step explanation:
Let's call the shorter side: x
Based on the information given in the problem, you know that:
Longer side: [tex]x+14[/tex]
Hypotenuse: [tex]2x-14[/tex]
- Apply the Pythagorean Theorem:
[tex]a^2=b^2+c^2[/tex]
Where a is the hypotenuse and b and c are the legs.
- Substitute values. Therefore, you obtain:
[tex](2x-14)^2=x^2+(x+14)^2[/tex]
- Solve for x. Keep on mind that:
[tex](a+b)^2=a^2+2ab+b^2\\\\(a-b)^2=a^2-2ab+b^2[/tex]
Then:
[tex](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[/tex]
Therefore, the length of the shorter leg is 42 feet.
