Data
Leg 1 = a = b + 3
Leg 2 = b
H = 15
Pythagorean theorem
15^2 = (b + 3)^2 + b^2
225 = b^2 + 6b + 9 + b^2
225 = 2b^2 + 6b + 9
2b^2 + 6b + 9 - 225 = 0
2b^2 + 6b - 216 = 0
Solving
b^2 + 3b - 108
Factoring
(b +12)(b - 9) = 0
b + 12 = 0 b -9 = 0
b = -12 b = 9
The length of b = 9 because there are not negative lengths
Leg 1 = 9 + 3
= 12
Leg 1 = 12
Leg 2 = 9
Hypotenuse = 15
Area = base x height / 2
= 12 x 9/2
= 54 u^2
