Name: Special Points of Concurrency
Uploaded: 2019-07-19
Duration: 8 min 2 s
Description: You may have heard about the special points of concurrency such as incentre, circumcentre, centroid, and orthocentre. Watch this video to learn about them in...

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 $5 \sqrt{2} cm$ .

Rashmi Bhartiya Solutions for Chapter: Triangle and Its Properties, Exercise 6: Worksheet - 37

Rashmi Bhartiya Mathematics Solutions for Exercise - Rashmi Bhartiya Solutions for Chapter: Triangle and Its Properties, Exercise 6: Worksheet - 37

Questions from Rashmi Bhartiya Solutions for Chapter: Triangle and Its Properties, Exercise 6: Worksheet - 37 with Hints & Solutions

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