Question

in the diagram below, \\( \triangle nml \sim \triangle kmj \\). find \\( y \\).

write your answer as a whole number or a decimal. do not round

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle NML\sim\triangle KMJ\), the ratios of corresponding sides are equal. That is \(\frac{NL}{KJ}=\frac{MN}{MK}\). Here \(NL = 23\) ft, \(MN=19\) ft, \(MK = 57\) ft, and \(KJ=y\).

Step2: Substitute values into the proportion

Substitute the values into \(\frac{NL}{KJ}=\frac{MN}{MK}\), we get \(\frac{23}{y}=\frac{19}{57}\).

Step3: Cross - multiply

Cross - multiply gives \(19y=23\times57\).

Step4: Solve for \(y\)

First, calculate \(23\times57 = 1311\). Then \(y=\frac{1311}{19}\).

Answer:

\(y = 69\)