Question
Draw an isosceles triangle ABC in which AB = AC = 6cm and BC = 5cm. Construct a triangle PQR similar to ABC in which PQ = 8cm. Also justify the construction.
✓
Answer
We have to draw,
$\triangle\text{PQR}\sim\triangle\text{ABC}$ $\text{PQ}=8\text{cm}$ $\therefore\frac{\text{PQ}}{\text{AB}}=\frac{8}{6}=\frac{4}{3}\ \ (\because\text{AB}=6\text{cm})$ So, PQ = QR = 8cm So, we have to draw $\triangle\text{PQR}\sim\triangle\text{ABC}$ with scale factor $\frac{4}{3}>1$ resulting $\triangle\text{PQR}$ will be larger than $\triangle\text{ABC}.$ Steps of Construction:
1. Draw $B C=5 cm$
2. Draw two arcs of 6 cm each from $B$ and $C$ in same direction let it be upside.
3. Join $A B$ and $A C$.
4. Draw acute $\angle CBX$ and mark $B , B _1, B_2, B_3, B_4$, with compass.
5. Join $B_3 C$ and draw $B_4 R \| B_3 C, R$ is on $B C$ produced.
6. Again, draw $R P \| C A$. $P$ is on $B A$ produced.
Therefore, $\triangle\text{PQR}\sim\triangle\text{ABC}$ with PQ = PR = 8cm. It's scale factor is $\frac{4}{3}.$
$\triangle\text{PQR}\sim\triangle\text{ABC}$ $\text{PQ}=8\text{cm}$ $\therefore\frac{\text{PQ}}{\text{AB}}=\frac{8}{6}=\frac{4}{3}\ \ (\because\text{AB}=6\text{cm})$ So, PQ = QR = 8cm So, we have to draw $\triangle\text{PQR}\sim\triangle\text{ABC}$ with scale factor $\frac{4}{3}>1$ resulting $\triangle\text{PQR}$ will be larger than $\triangle\text{ABC}.$ Steps of Construction:
1. Draw $B C=5 cm$
2. Draw two arcs of 6 cm each from $B$ and $C$ in same direction let it be upside.
3. Join $A B$ and $A C$.
4. Draw acute $\angle CBX$ and mark $B , B _1, B_2, B_3, B_4$, with compass.
5. Join $B_3 C$ and draw $B_4 R \| B_3 C, R$ is on $B C$ produced.
6. Again, draw $R P \| C A$. $P$ is on $B A$ produced.
Therefore, $\triangle\text{PQR}\sim\triangle\text{ABC}$ with PQ = PR = 8cm. It's scale factor is $\frac{4}{3}.$
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