Question

given $\triangle jkl \sim \triangle mnl$, find $jk$.

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle JKL\sim\triangle MNL\), the ratios of corresponding sides are equal. That is \(\frac{JM + ML}{ML}=\frac{JK}{MN}\). Here \(JM = 12\), \(ML=24\), and \(MN = 28\). First, find \(JL=JM + ML=12 + 24=36\).

Step2: Set up the proportion

We have the proportion \(\frac{JL}{ML}=\frac{JK}{MN}\). Substitute the values: \(\frac{36}{24}=\frac{JK}{28}\).

Step3: Solve for \(JK\)

Cross - multiply: \(24\times JK=36\times28\). Then \(JK=\frac{36\times28}{24}\). Simplify \(\frac{36}{24}=\frac{3}{2}\), so \(JK=\frac{3\times28}{2}=3\times14 = 42\).

Answer:

\(42\)