The perimeter of a right triangle is 30 inches. the longer leg is 2 more than twice the shorter leg. the hypotenuse is one more than the longer leg. find the area of the triangle?

s represents the shorter leg

3s - 9 represents the longer leg

2s + 1 represents the hypotenuse

(2s + 1)2 = s2 + (3s - 9)2                 Pythagorean Theorem

4s2 + 4s + 1 = s2 + 9s2 - 54s + 81  square binomial

4s2 + 4s + 1 = 10s2 - 54s + 81        combine like terms

0 = 6s2 - 58s + 80                           set to 0

0 =3s2 - 29s + 40                            divide both sides by 2

0 = (3s - 5)(s - 8)                             FOIL

{5/3, 8}

5/3 is not feasible since 3(5/3) - 9 is negative.

-by-step explanation: