Question

the figure shows a pair of similar triangles. find the lengths of the sides labeled with the variables. △jkl ~ △jts
answer
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lk =
js =

Explanation:

Step1: Use the property of similar triangles

For similar triangles \(\triangle JKL\sim\triangle JTS\), the ratios of corresponding sides are equal. That is \(\frac{LK}{TS}=\frac{LJ}{TJ}\). We know \(LJ = 16\), \(TJ=2\), and \(LK = 2x\), \(TS = 2\). Also, \(\frac{JK}{JS}=\frac{LJ}{TJ}\), where \(JK = 2x\), \(JS=x\), \(LJ = 16\), \(TJ = 2\).

From \(\frac{LJ}{TJ}=\frac{LK}{TS}\), substituting the values: \(\frac{16}{2}=\frac{2x}{2}\).

Step2: Solve for \(x\)

Cross - multiply the equation \(\frac{16}{2}=\frac{2x}{2}\).
Since \(\frac{16}{2}=8\) and \(\frac{2x}{2}=x\), we get \(x = 8\).

Step3: Find the lengths of \(LK\) and \(JS\)

For \(LK\), since \(LK = 2x\) and \(x = 8\), then \(LK=2\times8 = 16\).
For \(JS\), since \(JS=x\) and \(x = 8\), then \(JS = 8\).

Answer:

\(LK = 16\)
\(JS=8\)