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: Use the property of similar triangles

Since \(\triangle GHI\sim\triangle JKL\), the ratios of corresponding sides are equal. That is \(\frac{GH}{JK}=\frac{GI}{JL}\). Here \(GH = 49\), \(JK=23\), \(GI = 23\), and we need to find \(JL\).
So, \(\frac{49}{23}=\frac{23}{LJ}\).

Step2: Cross - multiply to solve for \(LJ\)

Cross - multiplying gives us \(49\times LJ=23\times23\).
Then \(LJ=\frac{23\times23}{49}\).
Calculate \(23\times23 = 529\), so \(LJ=\frac{529}{49}\approx10.8\).

Answer:

\(10.8\)