Question

find u.
write your answer as a whole number or a decimal. do not round.
u = \boxed{} meters

Explanation:

Step1: Identify similar triangles

Triangles $\triangle NOM$ and $\triangle NPL$ are similar (by AA similarity, as both have a right angle and share $\angle N$).

Step2: Set up proportion

Corresponding sides are proportional:
$$\frac{NM}{NL} = \frac{OM}{PL}$$
Substitute known values: $NM=4$, $NL=8$, $OM=3$, $PL=u$
$$\frac{4}{8} = \frac{3}{u}$$

Step3: Solve for $u$

Simplify $\frac{4}{8}=\frac{1}{2}$, then cross-multiply:
$$1 \times u = 2 \times 3$$
$$u=6$$

Answer:

$u=6$ meters