Question

triangle fgh is similar to triangle ijk. find ij. round your answer to the nearest tenth if necessary. figures are not drawn to scale.

Explanation:

Step1: Identify Corresponding Sides

Since \(\triangle FGH \sim \triangle IJK\), corresponding sides are proportional. Let's assume \(FG\) corresponds to \(IJ\) and \(HG\) corresponds to \(KJ\). So, \(\frac{FG}{IJ}=\frac{HG}{KJ}\).

Given \(FG = 13\), \(HG = 7\), \(KJ = 32\), and \(IJ = x\).

Step2: Set Up Proportion

Substitute the values into the proportion: \(\frac{13}{x}=\frac{7}{32}\).

Step3: Solve for \(x\)

Cross - multiply: \(7x=13\times32\).

Calculate \(13\times32 = 416\), so \(7x = 416\).

Then \(x=\frac{416}{7}\approx59.4\) (rounded to the nearest tenth).

Answer:

\(IJ\approx59.4\)