Question

Find the length of the hypotenuse

Answer 1

the hypotenuse is equal to 6

Answer 2

We know that : In a Triangle, If Two Angles are Equal then Corresponding Sides with Respect to those Two Angles Should be Equal.

In the Given Right Angled Triangle, There are Two Angles which are Equal to 45°. It means The Lengths of the Sides Corresponding to those Equal 45° Angles should be Equal.

It Means The Given Right Angled Triangle is also an Isosceles Triangle

⇒ The Other Side of the Triangle is $3\sqrt{2}$

As it is a Right Angled Triangle :

$\mathsf{\implies (Hypotenuse)^2 = (3\sqrt{2})^2 + (3\sqrt{2})^2}$

$\mathsf{\implies (Hypotenuse)^2 = 18 + 18}$

$\mathsf{\implies (Hypotenuse)^2 = 36}$

$\mathsf{\implies (Hypotenuse) = 6}$

The Length of Hypotenuse is 6