Question

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

Answer 1

Answer:

The value of x is 3.

Step-by-step explanation:

Given :

The lengths of sides of right angled triangle are x cm, (x + 1) cm and (x + 2) cm

To find :

the value of x

Solution :

In a right angled triangle, according to Pythagoras theorem,

• The square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.

 

In the given lengths of the sides, longest side = (x + 2) cm

 other two sides are x cm and (x + 1) cm

So,

(x + 2)² = x² + (x + 1)²

x² + 2² + 2(x)(2) = x² + x² + 1² + 2(x)(1)   [ ∵ (a + b)² = a² + b² + 2ab ]

x² + 4 + 4x = 2x² + 1 + 2x

2x² - x² = 4x - 2x + 4 - 1

 x² = 2x + 3

x² - 2x - 3 = 0

Solving the quadratic equation,

x² - 2x - 3 = 0

x² + x - 3x - 3 = 0

x(x + 1) - 3(x + 1) = 0

 (x + 1) (x - 3) = 0

• x + 1 = 0 ; x = -1
• x - 3 = 0 ; x = +3

⇒ x can not be negative as the length of the side can not be negative.

Hence, x = 3