Question

question
quadrilateral bcde is similar to quadrilateral fghi. find fg. round your answer to the nearest tenth if necessary. figures are not drawn to scale.
(images of quadrilaterals bcde and fghi with bcde having sides eb=17, bc=35 and fghi having side if=56, fg=x)

Explanation:

Step1: Identify Corresponding Sides

Since quadrilaterals \(BCDE\) and \(FGHI\) are similar, their corresponding sides are proportional. Let's assume \(BC\) corresponds to \(IF\) and \(BE\) corresponds to \(FG\). So, \(BC = 35\), \(IF = 56\), \(BE = 17\), and \(FG = x\).

Step2: Set Up Proportion

The proportion for similar figures is \(\frac{BE}{FG}=\frac{BC}{IF}\). Substituting the known values, we get \(\frac{17}{x}=\frac{35}{56}\).

Step3: Solve for \(x\)

Cross - multiply: \(35x = 17\times56\). Calculate \(17\times56 = 952\). Then, \(x=\frac{952}{35}\). Divide \(952\) by \(35\): \(x = 27.2\).

Answer:

\(27.2\)