Question

δjkl ~ δqrs

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle{JKL}\sim\triangle{QRS}\), the ratios of corresponding sides are equal. Let the unknown side \(KJ = x\). The ratio of \(KL\) to \(QS\) is equal to the ratio of \(KJ\) to \(QR\).

Step2: Set up the proportion

\(\frac{KL}{QS}=\frac{KJ}{QR}\). We know \(KL = 208\), \(QS=39\), \(QR = 33\). Substitute these values into the proportion: \(\frac{208}{39}=\frac{x}{33}\).

Step3: Solve the proportion for \(x\)

Cross - multiply: \(39x=208\times33\). Then \(x=\frac{208\times33}{39}\). Simplify \(\frac{208}{39}=\frac{16}{3}\) (dividing numerator and denominator by \(13\)), so \(x = 16\times11=176\).

Answer:

\(176\)