Question

The perimeter of two similar triangles $∆ABC$ and $∆PQR$ are $60cm$ and $36cm$ respectively. If $PQ=9cm,$then find the value of $AB.$

Answer 1

Finding the value of $AB$:

Given that $∆ABC$ $~$ $∆PQR$ .

Applying the property of similar triangles, when two triangles are similar then the ratio of their perimeter is equal to the ratio of their corresponding sides.

$$\begin{gathered} \frac{\mathrm{Perimeter}\mathrm{of}∆ABC}{\mathrm{Perimeter}\mathrm{of}∆PQR}=\frac{AB}{PQ}=\frac{BC}{QR}=\frac{CA}{RP} \\ \Rightarrow \frac{\mathrm{Perimeter}\mathrm{of}∆ABC}{\mathrm{Perimeter}\mathrm{of}∆PQR}=\frac{AB}{PQ} \\ \Rightarrow \frac{60}{36}=\frac{AB}{9}\left(\mathrm{given}\right) \\ \Rightarrow AB=\frac{60}{36}\times 9 \\ \Rightarrow AB=15cm \end{gathered}$$

Hence, the value of $AB$ is $15cm.$