Question

The perimeters of two similar triangles are $30cm$ and $20cm$ respectively. If one side of the first triangle is $12cm$ , determine the corresponding side of the second triangle.

Answer 1

We know that ,

When two triangles are similar

$\frac{PerimeterofTriangle1}{PerimeterofTriangle2}=\frac{SideofTriangle1}{SideofTriangle2}$

Given ,

Side of Triangle `$1=12cm$

$$\begin{gathered} PerimeterofTriangle1=30cm. \\ PerimeterofTriangle2=20cm \end{gathered}$$

let us assume the side of Triangle $2=xcm.$

$$\begin{gathered} \Rightarrow \frac{30}{20}=\frac{12}{x} \\ \Rightarrow \frac{3}{2}=\frac{12}{x} \\ \Rightarrow 3\times x=12\times 2 \\ \Rightarrow 3\times x=24 \\ \Rightarrow x=\frac{24}{3} \\ \Rightarrow x=8. \end{gathered}$$

Hence , side of Triangle $2$ = $8cm.$