Question

Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are $1\frac{1}{2}$ times the corresponding sides of the isosceles triangle.

Answer 1

Steps of Construction

Step 1. Draw a line segment BC = 8 cm.

Step 2. Draw the perpendicular bisector XY of BC, cutting BC at D.

Step 3. With D as centre and radius 4 cm, draw an arc cutting XY at A.

Step 4. Join AB and AC. Thus, an isosceles ∆ABC whose base is 8 cm and altitude 4 cm is obtained.

Step 5. Extend BC to E such that BE = $\frac{3}{2}$BC = $\frac{3}{2}\times 8$ cm = 12 cm.

Step 6. Draw EF || CA, cutting BA produced in F.


Here, ∆BEF is the required triangle similar to ∆ABC such that each side of ∆BEF is $1\frac{1}{2}\left(\mathrm{or}\frac{3}{2}\right)$ times the corresponding side of ∆ABC.