Question

question
triangle efg is similar to triangle hij. find the measure of side jh. round your answer to the nearest tenth if necessary.
g 25 f
19
e
j 12 i
h

Explanation:

Step1: Identify Corresponding Sides

Since \(\triangle EFG \sim \triangle HIJ\), corresponding sides are proportional. Side \(GF = 25\) in \(\triangle EFG\) corresponds to side \(IJ = 12\) in \(\triangle HIJ\), and side \(GE = 19\) in \(\triangle EFG\) corresponds to side \(JH\) in \(\triangle HIJ\).

Step2: Set Up Proportion

Let \(JH = x\). The proportion is \(\frac{GE}{JH}=\frac{GF}{IJ}\), so \(\frac{19}{x}=\frac{25}{12}\).

Step3: Solve for \(x\)

Cross - multiply: \(25x = 19\times12\). Calculate \(19\times12 = 228\). Then \(x=\frac{228}{25}\).

Step4: Compute the Value

\(\frac{228}{25}=9.12\), which rounds to \(9.1\) (to the nearest tenth).

Answer:

The measure of side \(JH\) is \(9.1\).