Question

1. the triangles △cde and △fge are similar. find the value of x, rounded to the nearest tenth.

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle CDE\sim\triangle FGE\), the ratios of corresponding sides are equal. That is \(\frac{CD}{FG}=\frac{CE}{FE}\). Here \(CD = 25\), \(CE=27\), \(FE = 40\), and \(FG=x\).
So we have the proportion \(\frac{25}{x}=\frac{27}{40}\).

Step2: Solve the proportion for \(x\)

Cross - multiply the proportion: \(27x=25\times40\).
First, calculate \(25\times40 = 1000\). Then the equation becomes \(27x = 1000\).
Solve for \(x\) by \(x=\frac{1000}{27}\approx37.0\).

Answer:

\(37.0\)