Question

the lengths of the sides of a triangle are xcm,(x+1)cm and (x+2)cm. determine x so that this triangle is a right angled triangle

Answer 1

hope the answer is correct

Answer 2

if it is a right angled triangle

(x+2)² = x² + (x+1)²
⇒ x² + 4x + 4 = x² + x² + 2x + 1
⇒ x² + 4x + 4 = 2x² + 2x + 1
⇒ 2x² - x² + 2x - 4x + 1 - 4 = 0
⇒ x² - 2x - 3 = 0
⇒ x² - 3x + x - 3  = 0
⇒ x(x-3) + 1(x-3) = 0
⇒ (x - 3)(x + 1) = 0
⇒ x = 3,  (-1 is not possible)

So x = 3.
Sides are 3,4,5