Question

a right triangle has one leg that is 2 inches longer than half the other leg. The length of the hypotenuse is √61 inches. Find the area of the triangle.

Answer 1

Answer: 18.72 square inches

Explanation:

(shorter leg)^2 + (longer leg)^2 = (hypotenuse)^2

x^2 + ((x/2) + 2)^2 = (√61)^2

x^2 + (x^2/4 + 2x + 4) = 61

4x^2 + x^2 + 8x + 16 = 244

5x^2 + 8x - 228 = 0

x = (-8 ± √(8^2 - 4(5)(-228))) / (2(5))

x ≈ 7.2

So the shorter leg of the right triangle is approximately 7.2 inches, and the longer leg is approximately 5.2 inches (since (x/2) + 2 = (7.2/2) + 2 = 5.2).

The area of the triangle is:

(1/2) * (shorter leg) * (longer leg)

= (1/2) * 7.2 * 5.2

= 18.72 square inches