Question

What is the measure of z?

Answer 1

Answer:

$3 \sqrt{13}$

Step-by-step 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

${6}^{2} + {9}^{2} = {r}^{2}$

$36 + 81 = {r}^{2}$

$117 = {r}^{2}$

$\sqrt{117} = r$

$\sqrt{9} \times \sqrt{13} = r$

$3 \sqrt{13} = r$