Question

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

Answer 1

Form given statement: $\Delta ABC\sim \Delta PQR$,

$PQ=12cm$

Perimeter of $\Delta ABC=AB+BC+CA=32cm$

Perimeter of $\Delta PQR=PQ+QR+RP=24cm$

Now,

$\frac{AB}{PQ}=\frac{BC}{QR}=\frac{CA}{RP}$

$=\frac{AB+BC+CA}{PQ+QR+RP}=\frac{32}{24}$

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

$AB=\frac{32\times 12}{24}=16cm$