Question

If the measures of sides of a triangle are $(x^2-1)cm,(x^2+1)cm$, and $2xcm$, then the triangle will be:

• A. right angled
• B. obtuse angled
• C. equilateral
• D. isosceles

Answer 1

The correct option is A right angled

Given that,

A triangle has three sides as $(x^2-1)cm,(x^2+1)cm$, and $2xcm$

To find out,

The type of triangle.

We can see that,

$(x^2-1{)}^2+(2x{)}^2=x^4+2x+1[\because (a-b{)}^2=a^2-2ab+b^2]$

$(x^2+1{)}^2=x^2+2x+1[\because (a+b{)}^2=a^2+2ab+b^2]$

Here, the square of the largest side of the triangle is equal to the sum of the squares of the other two sides.

Hence, by the converse of Pythagoras theorem, we can say that the given triangle is a right angled triangle.