Question

if uv = 21 and ux = 13, what is uw?
write your answer as a whole number or as a decimal rounded to the nearest hundredth.
uw =

Explanation:

Step1: Identify similar triangles

We have right triangle $\triangle UVW$ with altitude $VX$ to hypotenuse $UW$. By geometric mean theorem, $\triangle UVX \sim \triangle UWV$, so $\frac{UX}{UV} = \frac{UV}{UW}$.

Step2: Rearrange to solve for UW

Rearrange the proportion to isolate $UW$: $UW = \frac{UV^2}{UX}$

Step3: Substitute given values

Substitute $UV=21$, $UX=13$:
$UW = \frac{21^2}{13} = \frac{441}{13}$

Step4: Calculate decimal value

$\frac{441}{13} \approx 33.92$

Answer:

$33.92$