Question

Construct a triangle MNP, whose perimeter is 15 cm and whose sides are in the ratio 2:3:4.

Answer 1

Steps of construction:

Step I: Draw line segment XY = 15 cm (MN + NP + PM = 15 cm)

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

Step III: Locate 9 (= 2 + 3 + 4) points on ray XY at equal distances.

Step IV: Mark points R, S and T on XZ such that XR = 2 parts, RS = 3 parts and ST = 4 parts.

Step V: Join TY. Through R and S, draw RN|| TY and SP ||TY such that they intersect XY at N and P respectively.

Step VI: With N as the centre and NX as the radius, draw an arc.

Step VII: With P as the centre and PY as the radius, draw an arc that cuts the previous arc at M.

Step VIII: Join MN and MP. ΔMNP is the required triangle.