Question

triangle efg is similar to triangle hij. find the measure of side jh. round your answer to the nearest tenth if necessary.
g to f is 16, g to e is 29.9; j to i is 49, j to h is to be found.

Explanation:

Step1: Identify Corresponding Sides

Since \(\triangle EFG \sim \triangle HIJ\), corresponding sides are proportional. Side \(GF = 16\) corresponds to side \(IJ = 49\), and side \(EG = 29.9\) corresponds to side \(JH\) (let's call it \(x\)).

Step2: Set Up Proportion

The proportion is \(\frac{GF}{IJ}=\frac{EG}{JH}\), so \(\frac{16}{49}=\frac{29.9}{x}\).

Step3: Solve for \(x\)

Cross - multiply: \(16x = 49\times29.9\).
First, calculate \(49\times29.9 = 49\times(30 - 0.1)=49\times30-49\times0.1 = 1470 - 4.9 = 1465.1\).
Then, \(x=\frac{1465.1}{16}\approx91.6\).

Answer:

\(91.6\)