Question

Draw ∆ABC, right-angled at B, such that AB = 3 cm and BC = 4 cm. Now, construct a triangle similar to ∆ABC, each of whose sides is $\frac{7}{5}$ times the corresponding sides of ∆ABC.

Answer 1

Steps of Construction :

Step 1. Draw a line segment BC = 4 cm.
Step 2. With B as centre, draw an angle of 90^o.
Step 3. With B as centre and radius equal to 3 cm, cut an arc at the right angle and name it A.
Step 4. Join AB and AC.
Thus, △ ABC is obtained .
Step 5. Extend BC to D, such that BD = $\frac{7}{5}$ BC = $\frac{7}{5}$ (4) cm = 5.6 cm.
Step 6. Draw DE ∥ CA, cutting AB produced to E.



Thus, △EBD is the required triangle, each of whose sides is $\frac{7}{5}$ the corresponding sides of ∆ABC.