Question

δabc ~ δdef
find the value of x.
a
8 ft
× ft
e
3 ft
6 ft
x = ?

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle ABC\sim\triangle DEF\), the ratios of their corresponding sides are equal. That is \(\frac{BC}{EF}=\frac{AC}{DF}\).

Step2: Substitute the given values into the proportion

We know \(BC = 6\) ft, \(EF=3\) ft, \(AC = 8\) ft and \(DF=x\) ft. Substituting these values into \(\frac{BC}{EF}=\frac{AC}{DF}\), we get \(\frac{6}{3}=\frac{8}{x}\).

Step3: Cross - multiply to solve for \(x\)

Cross - multiplying gives \(6x=3\times8\). Then \(6x = 24\).

Step4: Solve for \(x\)

Divide both sides of the equation \(6x = 24\) by \(6\). So \(x=\frac{24}{6}\).

Answer:

\(x = 4\)