Question

consider triangle xyz with altitude wz. what is xz?
28
21
type the correct answer in the box. use numerals instead of words. if you need help, see this worked example
$xz =$

Explanation:

Step1: Find length of XW

$XW = XY - WY = 28 - 21 = 7$

Step2: Let $WZ = h$, $XZ = a$, $ZY = b$.

First use Pythagoras on $\triangle WZY$:
$h^2 + 21^2 = b^2$
$h^2 = b^2 - 441$

Step3: Use geometric mean theorem

For right triangles formed by altitude: $XW \times XY = a^2$
$a^2 = 7 \times 28$

Step4: Calculate $a$

$a^2 = 196$
$a = \sqrt{196} = 14$

Answer:

14