Question

Construct a triangle PQR, whose perimeter is 14 cm and whose sides are in the ratio 2:4:5.

Answer 1

Steps of construction:

Step I: Draw line segment XY = 14 cm (PQ + QR + RP = 14 cm)

Step II: Draw a ray XZ that makes an acute angle with XY in the downward direction.

Step III: Locate 11 (= 2 + 4 + 5) points on ray XY at equal distances.

Step IV: Mark points L, M and N on XZ such that XL = 2 parts, LM = 4 parts and MN = 5 parts.

Step V: Join NY. Through L and M, draw LQ|| NY and MR ||NY such that they intersect XY at Q and R respectively.

Step VI: With Q as the centre and QX as the radius, draw an arc.

Step VII: With R as the centre and RY as the radius, draw another arc that cuts the previous arc at P.

Step VIII: Join PQ and PR. ΔPQR is the required triangle.