Question

triangle def is similar to triangle ghi. find the measure of side hi. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Set up the proportion

Since \(\triangle DEF\sim\triangle GHI\), the ratios of corresponding sides are equal. Let \(HI = x\). Then \(\frac{DE}{GH}=\frac{EF}{HI}\). Substituting the values \(DE = 9\), \(GH=43\), \(EF = 19.3\), we get \(\frac{9}{43}=\frac{19.3}{x}\).

Step2: Cross - multiply

Cross - multiplying gives \(9x=43\times19.3\).

Step3: Calculate the right - hand side

\(43\times19.3 = 829.9\). So, \(9x = 829.9\).

Step4: Solve for \(x\)

Divide both sides by 9: \(x=\frac{829.9}{9}\approx92.2\).

Answer:

\(92.2\)