Question

if jl = 23 and kl = 15, what is lm?
write your answer as a whole number or as a decimal rounded to the nearest hundredth.
lm =
save answer

Explanation:

Step1: Identify similar triangles

We recognize that $\triangle JKL \sim \triangle KML$ (right triangles sharing $\angle L$, so AA similarity applies).

Step2: Set up proportion

Corresponding sides are proportional: $\frac{LM}{KL} = \frac{KL}{JL}$

Step3: Substitute given values

Plug in $JL=23$, $KL=15$:
$\frac{LM}{15} = \frac{15}{23}$

Step4: Solve for $LM$

Rearrange to isolate $LM$:
$LM = \frac{15^2}{23} = \frac{225}{23}$

Step5: Calculate decimal value

$\frac{225}{23} \approx 9.78$

Answer:

$9.78$