Answer:
Option D
Step-by-step explanation:
GIVEN :-
- Length of hypotenuse = 5 units
- Length of both the legs of the triangle = x units.
TO FIND :-
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.
[tex]=> 5^2 = x^2 + x^2[/tex]
[tex]=> 2x^2 = 5^2[/tex]
[tex]=> x^2 = \frac{5^2}{2}[/tex]
[tex]=> x = \sqrt{\frac{5^2}{2} } = \frac{5}{\sqrt{2} }[/tex]
Rationalizing the value ,
[tex]=> x = \frac{5}{\sqrt{2} } \times \frac{\sqrt{2} }{\sqrt{2} } = \frac{5\sqrt{2} }{2}[/tex]
