Question

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

Explanation:

Step1: Use the similarity of triangles

Since \(\triangle LKM\sim\triangle LON\) (by AA similarity, as \(\angle L\) is common and \(\angle LKM=\angle LON = 90^{\circ}\)), the ratios of corresponding sides are equal. That is \(\frac{MK}{NO}=\frac{LK}{LO}\).
We know \(LK = 4\) ft, \(LO=LK + KO=4 + 4=8\) ft, and \(MK = 3\) ft. Let \(NO=d\).
Substituting the values into the proportion \(\frac{3}{d}=\frac{4}{8}\).

Step2: Solve the proportion for \(d\)

Cross - multiply: \(4d=3\times8\).
So \(4d = 24\).
Divide both sides by 4: \(d=\frac{24}{4}\).

Answer:

\(d = 6\) feet