Question

What is the measure of z?

Answer 1

`3 √(13)`

Explanation:

Use altitude mean Theorem.

"If a triangle altitude splits it up into two right triangles and we are given the side left and right of the altitude then we can use the formula,

`{a}^(2) = lr`

where a is the altitude, l is the left side of the altitude and r is the right side of the altitude.

We are trying to find the value of a, and we know the lr is

4*9=36

`{a}^(2) = 36`

`a = 6`

So we know the altitude is 6.

Know since the right triangle form a right triangle, apply Pythagoren Theorem

`{6}^(2) + {9}^(2) = {r}^(2)`

`36 + 81 = {r}^(2)`

`117 = {r}^(2)`

`√(117) = r`

`√(9) * √(13) = r`

`3 √(13) = r`