Construct a triangle PQr whose sides are in the ratio of 2:3:4 and having a perimeter 13.5 cm . Give its justification

Perimeter = 13.5 cm

Let the 3 sides of the triangle be 2*x*, 3*x* and 4*x.*

Perimeter of triangle = 2*x* + 3*x* + 4*x*

⇒ 13.5 = 2*x* + 3*x* + 4*x*

⇒ 13.5 = 9*x*

⇒ *x* = 13.5/ 9

⇒ *x* = 1.5

Thus, sides of triangle are:

2(1.5) = 3.0 cm = 3 cm

3(1.5) = 4.5 cm

4(1.5) = 6.0 cm = 6 cm

Now, steps of construction are as follows:

Draw the line segment PQ of 6 cm.

Taking P as the centre and 3 cm as the radius draw an arc.

Taking Q as the centre and 4.5 cm as the radius draw an arc intersecting previous arc at R.

Join PR and QR.

PQR is the required triangle.

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