Using pythagoren therem and quadratic equation

Question

The length of the longer leg of a right triangle is 3 m more than three times the length of the shorter leg. The length of the hypotension is 4 m more than three times the length of the shorter leg find the lengths of the triangle

Answer 1

a= longer leg = 3 + 3s

s = shorter leg

h = hypotenuse = 4+ 3s

h^2 = a^2 +s^2

(4+3s)^2 = (3+3s)^1 + s^2

9s^2 +24s +16 = 9s^2 +18s + 9 + s^2

s^2 -6s - 7 = 0

(s-7)(s+1)=0

s= 7 meters

a= 24 meters

h= 25 meters

25^2=24^2+7^2

625=576+49