Question

What is the measure of n?

Answer 1

m = 10, n =
`√(75)`

Explanation:

We know that the value of an altitude of a right triangle is the square root of the values that the altitude split multiplied together (or the square root of the value of the bases multiplied together).

The values here would be 5 and 15. 5 times 15 is 75, so the value of the altitude is the square root of 75. To find the value of m, we can use the Pythagorean theorem, where 5 and n are the legs and m is the hypotenuse. We already know the value of n, so we can plug that into the Pythagorean theorem:

`5^2+(√(75))^2=m^2`

We know 5 squared is 25, and the square of the square root of 75 is 75, and 75 + 25 is 100.

`m^2=100`

This means that m is equal 10, because the square root of 100 is m.