Question

Find the length of the hypotenuse of a right triangle whose legs are 5 and sqare root of 2

Answer 1

2² + (√5)² = c²
4 + 5 = c²
9 = c²
c = 3

Sorry this is so late and was never answered. I just saw it pop up in the related questions.

Answer 2

The length of the hypotenuse is 3√3 units.

Explanation:

It is given that the length of the legs of a right triangle are 5 units and √2 units.

According to the Pythagoras theorem, in a right angled triangle

`(hypotenuse)^2=(leg_1)^2+(leg_2)^2`

Substitute leg₁=5 and leg₂=√2 in the above formula.

`(hypotenuse)^2=(5)^2+(√(2))^2`

`(hypotenuse)^2=25+2`

`(hypotenuse)^2=27`

Taking square root both the sides.

`hypotenuse=√(27)`

`hypotenuse=3√(3)`

Therefore the length of the hypotenuse is 3√3 units.