Question

Find the value of x. Express your answer in simplest radical form.

Answer 1

Option D

Explanation:

GIVEN :-

• Length of hypotenuse = 5 units
• Length of both the legs of the triangle = x units.

TO FIND :-

• Value of x

FACTS TO KNOW BEFORE SOLVING :-

Pythagoras Theorem states that measure of :-

Hypotenuse² = Base² + Perpendicular²

SOLUTION :-

The triangle given in the question is a right-angled triangle. So , Pythagoras theorem can be applied in it.

`=> 5^2 = x^2 + x^2`

`=> 2x^2 = 5^2`

`=> x^2 = (5^2)/(2)`

`=> x = \sqrt{(5^2)/(2) } = (5)/(√(2) )`

Rationalizing the value ,

`=> x = (5)/(√(2) ) * (√(2) )/(√(2) ) = (5√(2) )/(2)`