Question

Lengths of sides of a triangle are $3cm,4cm$ and $5cm$. The triangle is

• A. Obtuse angled triangle
• B. Acute-angled triangle
• C. Right-angled triangle
• D. An Isosceles right triangle

Answer 1

The correct option is C

Right-angled triangle

Identify the type of triangle based on given side lengths :

Given, lengths of sides of a triangle are $3cm,4cm$ and $5cm$

By the converse of the Pythagoras theorem,

We know that, if ${\left(hypotenuse\right)}^2={(adjacentside)}^2+{(oppositeside)}^2$, then the triangle is said to be a right angled triangle.

From the given data, hypotenuse $=5cm$

${\left(hypotenuse\right)}^2=5^2=25$

${(adjacentside)}^2+{(oppositeside)}^2=3^2+4^2$

$=9+16=25$

Thus, the Pythagoras theorem is satisfied

So, the given triangle is a right angled triangle.

Hence option $\left(C\right)$ is the correct answer.