Question

In a right angled triangle ABC, AB=x/2,BC=x+2 and CA=x+3,then x is equal to

Answer 1

Answer:

10 unit

Step-by-step explanation:

As ABC is a right-angled triangle, we can use Pythagoras theorem,

        Using Pythagoras theorem

⇒ CA² = AB² + BC²

⇒ (x + 3)² = (x/2)² + (x + 2)²

⇒ x² + 3² + 6x = x²/4 + x² + 2² + 4x

⇒ 9 + 6x = x²/4 + 4 + 4x

⇒ 0 = x²/4 + 4 - 9 + 4x - 6x

⇒ 0 = x²/4 - 5 - 2x

⇒ 0 = x² - 8x - 20

⇒ 0 = x² - 10x + 2x - 20

⇒ 0 = x(x - 10) + 2(x - 10)

⇒ 0 = (x - 10)(x + 2)

           Hence, x - 10 = 0

                        x = 10