Question

Draw a triangle of perimeter 13 centimetres and lengths of sides in the ratio 2 : 3 : 4.

Answer 1

First, we will divide a line segment of length 13 cm in the ratio 2:3:4.

The steps of construction are as follows:

1) Draw a line segment AB of length 13 cm.

2) Draw an acute angle, ∠YAB, at point A on the upper side of AB such that AY = 9 cm (sum of ratios).

3) Mark an arc on AY at a distance of 2 cm from A and name it as X.

4) Mark an arc on AY at a distance of 3 cm from X and name it as Z. The remaining length ZY = 9 cm − 2 cm − 3 cm = 4 cm.

5) Join YB and draw line segments XC and ZD parallel to YB.

We have obtained that AC:CD:DB = 2:3:4.

Thus, points C and D have divided line segment AB of length 13 cm in the ratio 2:3:4.

Now, we need to construct a triangle whose perimeter is 13 cm. Let the base of the required triangle is CD.

The steps of construction are as follows:

1) Taking C as the centre and CA as the radius, mark an arc on the lower side of AB.

2) Taking D as the centre and DB as the radius, mark an arc cutting the previously drawn arc at point E.

3) Join CE and DE.

ΔCDE thus obtained has perimeter 13 cm.