Question

One leg of a right triangle is 3 more inches than he shorter leg. The hypotenuse is 15 inches. What are the lengths of the legs of the triangle and what is its area? Leg 1Leg 2Area

Answer 1

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