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

1. 9 inches, 12 inches and 15 inches

2. 54 square inches

Step-by-step explanation:

1. The first part of this question would lead to a quadratic equation. Let the shorter leg be represented by x.

shorter leg = x

other leg = x + 3

hypotenuse = 15 inches

Applying the Pythagoras theorem, we have;

= +

225 = +

225 = + + 6x + 9

       = 2 + 6x + 9

2 + 6x + 9 - 225 = 0

2 + 6x - 216 = 0

divide through by 2 to have

+ 3x - 108 = 0

From the quadratic formula;

x = (-b ± ) ÷ 2a

but, a = 1, b = 3, c = -108

x = (-3 ± ) ÷ 2

  = (-3 ± ) ÷ 2

= (-3 ± 21) ÷ 2

Thus,

x = (-3 + 21) ÷ 2 OR x = (-3 - 21) ÷ 2

x = 9 OR x = -12

So that, x = 9 inches

The shorter leg is 9 inches, and the other leg is 12 inches.

2. The area of the triangle can be determined by applying Heron's formula:

A =

where s is the average value of the sum of the three sides a, b, and c.

Let, a = 9, b = 12 and c = 15

s =

  =

  = 18

A =

   =

   =

A = 54

Area of the triangle is 54 square inches.

-2/