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 square of the hypotenuse of a right-angled isosceles triangle is $200 m$ . Find the length of the sides.

Accepted Answer

The square of the hypotenuse of a right-angled isosceles triangle is $200 m$ .

We have to find the length of the sides.

In an isosceles right-angled triangle, the two sides on the right angle are equal

Let the equal side be $a$ .

In the isosceles right triangle, the base and height $= a m$

By using Pythagoras theorem,

'The square on the hypotenuse is equal to the sum of the squares on the other two sides'.

$\Rightarrow {(H y p o t e n u s e)}^{2} = {(P e r p e n d i c u l a r)}^{2} + {(B a s e)}^{2}$

$\Rightarrow {(H y p o t e n u s e)}^{2} = 200$

$\Rightarrow 200 = a^{2} + a^{2} = 2 a^{2}$

$\Rightarrow 200 = 2 a^{2}$

$\Rightarrow a^{2} = \frac{200}{2} = 100$

$\Rightarrow a = \sqrt{100} = 10 m$

Hence, the length of the sides are $10 c m$ each.

Vaishali Bhatia and Rupesh Pathak Solutions for Chapter: Triangles, Exercise 5: HOTS

Vaishali Bhatia Mathematics Solutions for Exercise - Vaishali Bhatia and Rupesh Pathak Solutions for Chapter: Triangles, Exercise 5: HOTS

Questions from Vaishali Bhatia and Rupesh Pathak Solutions for Chapter: Triangles, Exercise 5: HOTS with Hints & Solutions

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