Question

find d.
write your answer as a whole number or a decimal. do not round.
d = yards

Explanation:

Step1: Determine the ratio of the sides

Since \(\triangle JIK\) and \(\triangle JML\) are similar (by AA similarity, as \(\angle JIK=\angle JML = 90^{\circ}\) and \(\angle J\) is common). The ratio of the corresponding sides of similar triangles is equal. The ratio of the vertical sides is \(\frac{JI}{JM}=\frac{8}{8 + 16}=\frac{8}{24}=\frac{1}{3}\).

Step2: Use the ratio to find \(d\)

Let the horizontal side of the smaller triangle be \(IK = 15\) yd and the horizontal side of the larger triangle be \(ML=d\). Since the ratio of the sides of similar triangles \(\frac{IK}{ML}=\frac{JI}{JM}\), substituting the values we get \(\frac{15}{d}=\frac{1}{3}\). Cross - multiplying gives \(d=15\times3\).

Answer:

\(d = 45\) yards