Question
Construct an isosceles triangle whose base is 8cm and altitude 4cm and then another triangle whose sides are $1\frac12\text{times}$ the corresponding sides of the isosceles triangle.
✓
Answer
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 centre and radius 4cm, draw an arc cutting XY at A.
Step 4. Join AB and AC. Thus, an isosceles $\triangle\text{ABC}$ whose base is 8cm and altitude 4cm is obtained.
Step 5. Extend BC to E such that $\text{BE}=\frac{3}{2}\text{BC}=\frac32\times8\text{cm}=12\text{cm}.$
Step 6. Draw EF || CA, cutting BA produced in F.
Here, $\triangle\text{BEF}$ is the required triangle similar to $\triangle\text{ABC}$ such that each side of $\triangle\text{BEF}$ is $1\frac12$ or $\Big(\frac32\Big)\text{times}$ the corresponding side of $\triangle\text{ABC}.$
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