Question

quadrilateral cdef is similar to quadrilateral ghij. find the measure of side hi. round your answer to the nearest tenth if necessary. figures are not drawn to scale.

Explanation:

Step1: Set up the proportion

Since the quadrilaterals are similar, the ratios of corresponding sides are equal. Let \(HI = x\). The proportion is \(\frac{CD}{GH}=\frac{DE}{HI}\). Here, \(CD = 23\), \(DE = 15\), \(GH = 10\). So the proportion becomes \(\frac{23}{10}=\frac{15}{x}\).

Step2: Cross - multiply

Cross - multiplying gives \(23x=15\times10\).

Step3: Solve for \(x\)

\(23x = 150\), then \(x=\frac{150}{23}\approx6.5\).

Answer:

\(6.5\)