Question

shows a pair of similar triangles. find the lengths of the sides labeled with the variables. $\triangle jkl sim \triangle jts$

your answer (opens in new window)

$lk = square$

$js = square$

Explanation:

Step1: Set up proportion

Since \(\triangle JKL\sim\triangle JTS\), the ratios of corresponding sides are equal. So, \(\frac{LK}{TS}=\frac{LJ}{TJ}\). Substituting the values, we get \(\frac{5x}{5}=\frac{16}{x}\).

Step2: Cross - multiply

Cross - multiplying the proportion \(\frac{5x}{5}=\frac{16}{x}\) gives \(5x\times x = 5\times16\), which simplifies to \(5x^{2}=80\).

Step3: Solve for \(x\)

Divide both sides of \(5x^{2}=80\) by \(5\): \(x^{2}=\frac{80}{5} = 16\). Then take the square root of both sides. Since \(x\) represents a length, \(x = 4\) (we ignore \(x=- 4\) as length cannot be negative).

Step4: Find \(LK\) and \(JS\)

Substitute \(x = 4\) into \(LK = 5x\), so \(LK=5\times4 = 20\). And \(JS=x\), so \(JS = 4\).

Answer:

\(LK = 20\), \(JS = 4\)