Question

Construct an isosceles triangles whose base is 8 cm and altitude 4 cm and then another triangle whose sides are`1/2` times the corresponding sides of the isosceles triangle.

Answer 1

Steps of Construction
Step 1: Draw a line segment BC = 8cm.
Step 2: Draw the perpendicular bisector XY of BC, cutting BC at D.
Step 3: With D as center and radius 4 cm, draw an arc cutting XY at A.
Step 4: Join AB and AC. Thus, an isosceles ΔABC whose base is 8 cm and altitude 4 cm is obtained.
Step 5: Extend BC to E such that=`3/2 BC = 3/1 xx 8cm = 12 cm.`
 Step 6: Draw EF ||CA, cutting BA produced in F.

Here, ΔBEF is the required triangle similar to ΔABC such that each side of ΔBEF is `1 1/2 (or 3/2 )`  times the corresponding side of Δ ABC.