The longer leg of a right triangle is 3 inches more than 3 times the length of the shorter leg. The area of the triangle is 84 square inches. How do you find the perimeter of a right triangle?

P = 56 square inches.

Explanation:

See figure below for better understanding.

$c = 3 b + 3$

$\frac{b . c}{2} = 84$

$\frac{b . \left(3 b + 3\right)}{2} = 84$

$3 {b}^{2} + 3 b = 84 \times 2$

$3 {b}^{2} + 3 b - 168 = 0$

${b}_{1} = 7$
${b}_{2} = - 8$ (impossible)

So, $b = 7$

$c = 3 \times 7 + 3 = 24$

${a}^{2} = {7}^{2} + {24}^{2}$

${a}^{2} = 625$

$a = \sqrt{625} = 25$

$P = 7 + 24 + 25 = 56$ square inches