Question

In right triangle ABC, angle C = 90 degrees, c = 3, and a + b = square root of 17. Compute the area of the triangle.

Answer 1

2

Explanation:

Given in the question,

a + b = √17

(a+b)² = 17

a² + b² +2ab = 17

a² + b² = 17 - 2ab

Area of triangle

1/2 (h)(b)

here h is perpendicular height of triangle = a

b is the base of triangle = b

Use pythagorus theorem:

hypotenuse² = base² + height²

3² = a² + b²

9 = a² + b²

9 = 17 - 2ab

9 - 17 = -2ab

-8 = -2ab

cancel minus on both sides

8 = 2ab

ab = 8/2

ab = 4

Plug ab in the formula of area

1/2 (h)(b)

1/2 (a)(b)

1/2 (4)

4/2

2