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 2x, 3x and 4x.
Perimeter of triangle = 2x + 3x + 4x
⇒ 13.5 = 2x + 3x + 4x
⇒ 13.5 = 9x
⇒ 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.