Question

The perimeters of two similar triangles $ABC$ and $PQR$ are $32cm$ and $24cm$. If $PQ=12cm$, find $AB$.

Answer 1

Step 1: Note the given data

Given that $△ABC$ and $△PQR$ are similar.

Perimeter of $△ABC=32cm$

Perimeter of $△PQR=24cm$

The length of $PQ=12cm$

Step 2: Finding the length of $AB$

Similar Triangles property: The perimeter of similar triangles bears the same ratio as their corresponding sides.

So, $△ABC~$$△PQR$

$\Rightarrow \frac{Perimeterof△ABC}{Perimeterof△PQR}=\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}$

From the given data, we get

$\frac{32}{24}=\frac{AB}{PQ}$

$\Rightarrow \frac{AB}{12}=\frac{32}{24}\left[\because PQ=12\right]$

$\Rightarrow AB=\frac{32\times 12}{24}$

$\Rightarrow AB=16cm$

Hence, the length of $AB$ is $16cm$.