Question

Please solve and show work.

Answer 1

Answer:

63.16 in approx.

Step-by-step explanation:

Let the shorter leg be S.  Then the longer leg is L = 3S + 3.

The formula for the area of a triangle is A = (1/2)(base)(height).  Here, that works out to A = 84 in^2 = (1/2)(S)(3S + 3).

Simplifying, we get 168 in^2 = S(3S + 3), or

3S^2 + 3S - 168 = 0, or

 S^2  +  S  - 56   = 0.  This factors as follows:  (S - 8)(S + 7) = 0, so the positive root is S = 8.  We discard the negative root.

Thus, the shorter leg length is 8 and the longer leg length is 3(8) + 3, or 27.

According to the Pythagorean Theorem, the hypotenuse length is given by

L^2 = 8^2 + 27^2, or

L^2 = 64 + 729 = 793.

L = hypotenuse length = √793, or approx. 28.2 in.

Then the perimeter of the triangle is 8 + 27 + 28.2 in, or approx. 63.16 in