Question

Draw an isosceles triangle ABC in which AB=AC =6 cm and BC 5cm. Construct a triangle PQR similar to $\Delta$ ABC in which PQ=8 cm. Also justify the construction.

Answer 1

We have to draw

$\Delta PQR\sim \Delta ABC$

$PQ=8cm$

$\therefore \frac{PQ}{AB}=\frac{8}{6}=\frac{4}{3}$ $(\because AB=6cm)$

So, $PQ=QR=8cm$

So, we have to draw $\Delta PQR\sim \Delta ABC$ with scale factor $\frac{4}{3}>1$ resulting $\Delta PQR$ will be larger than $\Delta ABC$.

REF. IMAGE

Steps of Construction :

(i) Draw $BC=5cm$

(ii) Draw two arcs of $6cm$ each from B and C same direction let it be upside.

(iii) Join AB and AC.

(iv) Draw acute $\angle CBX$ and mark $B,B_1,B_2,B_3,B_4$ with compass.

(v) Join $B_{3}C$ and draw $B_{4}R||B_{3}C,R$ is on $BC$ produced.

(vi) Again, draw $RP||CA$. P is on $BA$ produced.

Therefore, $\Delta PQR\sim \Delta ABC$ with $PQ=PR=8cm$. It's scale factor is $\frac{4}{3}$.