Question

What is the hypotenuse in an isosceles right-angled triangle is equal to?

Answer 1

Find the hypotenuse of the isosceles right-angled triangle

Since it is given that the triangle is isosceles so we know that the two sides of the isosceles triangle are equal.

Let the equal side be $a$.

Pythagoras's theorem states that: $hypotenuse=\sqrt{bas{e}^2+heigh{t}^2}$

Now, the hypotenuse of the isosceles right-angled triangle will be,

$$\begin{gathered} hypotenuse=\sqrt{a^2+a^2} \\ \Rightarrow hypotenuse=\sqrt{2a^2} \\ \Rightarrow hypotenuse=\sqrt{2}a \end{gathered}$$

Hence, the hypotenuse of the isosceles right-angled triangle is $\sqrt{2}\times$length of similar side.