Question

1.The lengths of sides of triangle are x cm,(x + 1) cm and (x + 2) cm, the value of x when triangle is right angled is *

Answer 1

Given: The lengths of sides of triangle are x cm,(x + 1) cm and (x + 2) cm

To find:  The value of x when triangle is right angled.

Solution:

• Now the sides are: x cm,(x + 1) cm and (x + 2) cm

• If triangle is right angled, then we can apply Pythagoras theorem.

• We get:

                   x² + (x + 1)² = (x + 2)²

• Expanding it, we get:

                   x² + x² + 2x + 1 = x² + 4x + 4

                   x² + 2x + 1 = 4x + 4

                   x² - 2x - 3 = 0

• For x, we have:

                   -(-2) ± √((-2)² - 4(1)(-3)) / 2

                   2 ± √4+12 / 2

                   2 ± √16 / 2

                   2 ± 4 / 2

                   6/2 , -2/2

                   x = 3, -1

• Negative value is discarded, so x is 3.

Answer:

               So the value of x is 3.