Question

triangle ghi is similar to triangle jkl. find the measure of side lj. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Identify corresponding sides

Since \(\triangle GHI \sim \triangle JKL\), the corresponding sides are proportional. So, \(\frac{IH}{KL}=\frac{GI}{LJ}\). Here, \(IH = 13.6\), \(KL = 48\), and \(GI = 21\). Let \(LJ = x\).

Step2: Set up the proportion

We have the proportion \(\frac{13.6}{48}=\frac{21}{x}\).

Step3: Cross - multiply to solve for \(x\)

Cross - multiplying gives \(13.6x=48\times21\). First, calculate \(48\times21 = 1008\). Then, \(x=\frac{1008}{13.6}\).

Step4: Calculate the value of \(x\)

\(\frac{1008}{13.6}\approx74.1\) (rounded to the nearest tenth).

Answer:

\(74.1\)