Question

Construct a triangle ABC, whose perimeter is 13 cm and whose sides are in the ratio 3:4:5.

Answer 1

Steps of construction:

Step I: Draw line segment XY = 13 cm (AB + BC + CA = 13 cm)

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

Step III: Locate 12 (= 3 + 4 + 5) points on ray XY at equal distances.

Step IV: Mark points L, M and N on XZ such that XL = 3 parts, LM = 4 parts and MN = 5 parts.

Step V: Join NY. Through L and M, draw LB|| NY and MC ||NY such that they intersect XY at B and C respectively.

Step VI: With B as the centre and BX as the radius, draw an arc.

Step VII: With C as the centre and CY as the radius, draw another arc that cuts the previous arc at A.

Step VIII: Join AB and AC. ΔABC is the required triangle.