Question

triangle efg is similar to triangle hij. find the measure of side jh. round your answer to the nearest tenth if necessary. figures are not drawn to scale. e f: 13, e g:25; h i:53

Explanation:

Step1: Identify corresponding sides

Since \(\triangle EFG \sim \triangle HIJ\), the corresponding sides are proportional. So, \(\frac{EF}{HI}=\frac{EG}{JH}\). Here, \(EF = 13\), \(HI = 53\), and \(EG = 25\). Let \(JH=x\).

Step2: Set up proportion and solve

We have the proportion \(\frac{13}{53}=\frac{25}{x}\). Cross - multiply to get \(13x=53\times25\). Calculate \(53\times25 = 1325\). Then, \(x=\frac{1325}{13}\approx101.9\).

Answer:

\(101.9\)