Question

The three sides of a right-angled triangle are x, x+1 and 5. Find x and the area, if the longest side is 5.

Answer 1

x = 3

area = 6

Explanation:

using phytagoras's. theorem

a² + b² = c² (with c is the longest one)

x² + (x+1)² = 5²

x² + x² + 2x + 1 = 25

2x² + 2x - 24 = 0 (divide all by 2)

x² + x -12 = 0 then factorize

(x-3)(x+4) = 0

we get x = 3 and x = -4. Take the positive one.

so now we have x = 3 then x + 1 must be 4.

the area is

A = ½ . 3 . 4 = 6