Question

r
s
304
m
l
32
28
24
266
q
?

Explanation:

Step1: Find the ratio of similarity

Since \(ML\parallel RS\), \(\triangle QML\sim\triangle QRS\). The ratio of similarity \(k=\frac{QM}{QR}\). Given \(QM = 28\), \(QR=28 + 266=294\), so \(k=\frac{28}{294}=\frac{1}{10.5}\)

Step2: Use the property of similar triangles for the side \(QS\)

Let the length of the unknown side be \(x\). We know that \(\frac{QL}{QS}=k\). Also, \(QL = 24\). Let \(QS=24 + x\). Then \(\frac{24}{24 + x}=\frac{1}{10.5}\)

Cross - multiply: \(24\times10.5=24 + x\)

\(252=24+x\)

Subtract 24 from both sides: \(x = 252-24=228\)

Answer:

\(228\)