Question

if △cde ~ △fge, find the value of x.
a 1080
b 43.2
c 37
d 16.875

Explanation:

Step1: Use the property of similar triangles

For similar triangles \(\triangle CDE\sim\triangle FGE\), the ratios of corresponding sides are equal. So, \(\frac{DE}{GE}=\frac{CE}{FE}\).

Step2: Substitute the known values

We know \(DE = 25\), \(GE=40\), \(CE = 27\), and \(FE=x\). Substituting into the proportion \(\frac{25}{40}=\frac{27}{x}\).

Step3: Cross - multiply

Cross - multiplying gives \(25x=27\times40\).

Step4: Solve for \(x\)

First, calculate \(27\times40 = 1080\). Then \(x=\frac{1080}{25}=43.2\).

Answer:

B. \(43.2\)