the longer leg of a right triangle is 8 inches more than 4 times the shorter leg. If the area is 160 square inches then find the perimeter

Question

Help need this done fast

Answer 1

If the shorter leg is length x, the other leg is 4x+8 inches long.

The area is half the product of these legs: x(4x+8)/2=160, x(2x+4)=160.

This can be further simplified: x(x+2)=80, so x²+2x-80=0=(x+10)(x-8).

The only positive solution is x=8 inches, so the other leg is 4×8+8=40 inches.

The hypotenuse is √(64+1600)=√1664=8√26=40.79 inches approx.

The perimeter is 8+40+8√26=48+40.79=88.79 in approx.