Question

How do you find the length of the hypotenuse of a triangle with sides of length √5m and 3√2m?

Answer 1

`sqrt(23)`

Explanation:

A right-angled triangle with legs of lengths `a` and `b`, and a hypotenuse of `c` has the lengths of its sides specified by the Pythagorean Theorem:
`color(white)("XXX")c^2=a^2+b^2`

For the given case `a=sqrt(5) m` and `b=3sqrt(2) m`

Therefore
`color(white)("XXX")c^2=(sqrt(5))^2+(3sqrt(2))^2`

`color(white)("XXXX")=5+18`

`color(white)("XXXX")=23`

So
`color(white)("XXX")c=sqrt(23)`