Answer:
The length of the leg along the wall of the right triangle is 8 feet
The length of the hypotenuse of the right triangle is 17 feet
The length of the other leg (third side) of the right triangle is 15 feet
Step-by-step explanation:
Let
x ----> the leg along the wall of the right triangle
y-----> the hypotenuse of the right triangle
z ----> the other leg (third side) of the right triangle
we know that
----> equation A
----> equation B
Applying the Pythagorean Theorem
----> equation C
Solve the system by substitution
substitute equation A and equation B in equation C
![(x+9)^2=x^2+(x+7)^2](https://tex.z-dn.net/?f=%28x%2B9%29%5E2%3Dx%5E2%2B%28x%2B7%29%5E2)
solve for x
![x^2+18x+81=x^2+x^2+14x+49\\2x^2-x^2+14x-18x+49-81=0\\x^2-4x-32=0](https://tex.z-dn.net/?f=x%5E2%2B18x%2B81%3Dx%5E2%2Bx%5E2%2B14x%2B49%5C%5C2x%5E2-x%5E2%2B14x-18x%2B49-81%3D0%5C%5Cx%5E2-4x-32%3D0)
Solve the quadratic equation by graphing
using a graphing tool
The solution is x=8
see the attached figure
<em>Find the value of y</em>
![y=8+9=17\ ft](https://tex.z-dn.net/?f=y%3D8%2B9%3D17%5C%20ft)
<em>Find the value of z</em>
![z=8+7=15\ ft](https://tex.z-dn.net/?f=z%3D8%2B7%3D15%5C%20ft)
therefore
The length of the leg along the wall of the right triangle is 8 feet
The length of the hypotenuse of the right triangle is 17 feet
The length of the other leg (third side) of the right triangle is 15 feet