Question

If the sides of the right angled triangle is x+2, x+1, x then what is the value of x?

(a) 1

(b) 2

(c) 3

(d) 4

I had been asked this question during an interview.

Question is taken from Solution of Quadratic Equation by Factorisation topic in chapter Quadratic Equation of Mathematics – Class 10

Answer 1

The correct option is (a) 1

Explanation: Sides of the right angled triangle is x+2, x+1, x

From Pythagoras theorem,

hyp^2=adj^2+base^2

(x+2)^2=(x+1)^2+(x)^2

x^2+4x+4=x^2+1+2x+x^2

4x+4=x^2+1+2x

x^2-2x-3=0

x^2+3x-x-3=0

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

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

x=1, -3

Since, sides of triangle cannot be negative.

Hence, x=1