Question

triangle ghi is similar to triangle jkl. find the measure of side lj. round your answer to the nearest tenth if necessary.
(image of two triangles: triangle ghi with side gi = 31, side ih = 17; triangle jkl with side kl = 58)

Explanation:

Step1: Identify corresponding sides

Since \(\triangle GHI \sim \triangle JKL\), the sides are proportional. Corresponding sides: \(IH\) corresponds to \(KL\), and \(IG\) corresponds to \(LJ\). So \(IH = 17\), \(KL = 58\), \(IG = 31\), and \(LJ\) is unknown (\(x\)).

Step2: Set up proportion

Proportion: \(\frac{IH}{KL}=\frac{IG}{LJ}\) → \(\frac{17}{58}=\frac{31}{x}\)

Step3: Solve for \(x\)

Cross - multiply: \(17x = 58\times31\)
Calculate \(58\times31 = 1798\)
Then \(x=\frac{1798}{17}\approx105.8\)

Answer:

\(105.8\)