Question

A side of an isosceles right angled triangle is x/2 then find the hypotenuse.​

Answer 1

Step-by-step explanation:

Given :-

A side of an isosceles right angled triangle is

x/2 units

To find :-

Find the hypotenuse ?

Solution :-

Given that

The side of an isosceles right angled triangle

= x/2 units

Let consider ∆ABC is an Isosceles right angled triangle

AB = BC = x/2 units

AC is the hypotenuse

By Pythagorous Theorem,

Hypotenuse² = Side² + Side²

=> AC² = AB² + BC²

=> AC² = (x/2)²+(x/2)²

=> AC² = (x²/4)+(x²/4)

=> AC² = (x²+x²)/4

=> AC² = 2x²/4

=> AC² = x²/2

=> AC = √(x²/2)

=> AC = x/√2 units or

=> AC = (x/√2)×(√2/√2)

=> AC = √2 x/2 units

Solution :-

The length of the hypotenuse = x/√2 units or

(√2 x) /2 units

Used formulae:-

Pythagoras Theorem:-

In a right angled triangle, The square of the hypotenuse is equal to the sum of the squares of the other two sides ".

Isosceles right angled triangle:-

The two sides are equal in a right angled triangle is called Isosceles right angled triangle.