Draw ∆ABC in which BC = 5.4 cm, ∠B = 45° and ∠A = 105°. Now, construct a triangle similar to ∆ABC, each of whose sides is $\frac{4}{3}$ the corresponding side of ∆ABC.

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Solution

Steps of Construction :

Step 1. Draw a line segment BC = 5.4 cm.
Step 2. With B as centre, draw an angle of 45^o .
Step 3. With C as centre, draw an angle measuring $180 ° - (105 ° + 45 °) = 30 °$ .
Step 4. Name the point of intersection A.
Step 5. Join AB and AC.
Thus, △ABC is obtained .
Step 6. Extend BC to D, such that BD = $\frac{4}{3}$ BC = $\frac{4}{3}$ (5.4) cm = 7.2 cm.
Step 7. Draw DE ∥ AC, cutting AB produced to E.

Thus, △EBD is the required triangle, each of whose sides is $\frac{4}{3}$ the corresponding sides of ∆ABC.

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