Question

Construct a ∆ABC, in which BC = 5 cm, ∠C = 60° and altitude from A is equal to 3 cm. Construct a ∆ADE similar to ∆ABC, such that each side of ∆ADE is $\frac{3}{2}$ times the corresponding side of ∆ABC. Write the steps of construction.

Answer 1

Steps of Construction :

Step 1. Draw a line l .
Step 2. Draw an angle of 90^o at M on l .
Step 3. Cut an arc of radius 3 cm on the perpendicular. Mark the point as A.
Step 4. With A as centre, make an angle of 30^o and let it cut l at C. We get $\angle ACB=60°$.
Step 5. Cut an arc of 5 cm from C on l and mark the point as B.
Step 6. Join AB.
Thus, △ABC is obtained .
Step 7. Extend AB to D, such that BD =$\frac{1}{2}$ BC.
Step 8. Draw DE $\parallel BC$, cutting AC produced to E.



Then, △ADE is the required triangle, each of whose sides is $\frac{3}{2}$of the corresponding sides of △ABC.