Name: Triangle Inequality Theorem
Uploaded: 2019-07-19
Duration: 5 min 58 s
Description: Measure the sum of lengths of two sides of a triangle and you'll find it to be greater than the length of the other side. Learn more about triangle inequalit...

Question

The two sides of a right angled triangle are equal and square of its hypotenuse is

50 {cm}^{2}

. Find the length of each side.

Accepted Answer

Given that the two sides of a right-angled triangle are equal. Hence, it is the right isosceles triangle. Also, given that the square of its hypotenuse is $50 {cm}^{2}$ . We have to find the length of each side.

Let the length of each equal side of the right isosceles triangle be $x cm$ .

Using Pythagoras theorem on $△ A B C$ , we obtain, $A B^{2} + B C^{2} = A C^{2}$

$\Rightarrow x^{2} + x^{2} = 50$

$\Rightarrow 2 x^{2} = 50$

$\Rightarrow x^{2} = \frac{50}{2} = 25$

$\Rightarrow x = \sqrt{25} = 5 cm$ .

The length of the hypotenuse $= \sqrt{50} = \sqrt{2 \times 5 \times 5} = 5 \sqrt{2} cm$ .

Therefore, the length of each of the two equal sides of the triangle is $5 cm$ and the length of the hypotenuse is $5 \sqrt{2} cm$ .

The two sides of a right angled triangle are equal and square of its hypotenuse is $50 {cm}^{2}$ . Find the length of each side.

Important Questions on Triangle and Its Properties

Learn and Prepare for any exam you want !

The two sides of a right angled triangle are equal and square of its hypotenuse is 50 cm2. Find the length of each side.

Important Questions on Triangle and Its Properties

Learn and Prepare for any exam you want !

The two sides of a right angled triangle are equal and square of its hypotenuse is $50 {cm}^{2}$ . Find the length of each side.