# Constructions

#### Question 4:

Construct an isosceles
triangle whose base is 8 cm and altitude 4 cm and then another
triangle whose side are **
**times the corresponding sides of the isosceles triangle.

Give the justification of the construction.

#### Answer:

Let us assume that ΔABC is an isosceles triangle having CA and CB of equal lengths, base AB of 8 cm, and AD is the altitude of 4 cm.

A ΔAB'C' whose sides are times of ΔABC can be drawn as follows.

**Step 1**

Draw a line segment AB of 8 cm. Draw arcs of same radius on both sides of the line segment while taking point A and B as its centre. Let these arcs intersect each other at O and O'. Join OO'. Let OO' intersect AB at D.

**Step 2**

Taking D as centre, draw an arc of 4 cm radius which cuts the extended line segment OO...

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