Question

Construct a ∆ABC whose perimeter is 15 cm and sides are in the ratio 3 : 4 : 5.

Answer 1

Steps of construction:
1. Draw a line segment XY = 15 cm.
2. Construct an acute angle with XY in the downward direction.
3. With X, set off (3 + 4 + 5) = 12 equal distances along XP.
4. Mark points L, M and N such that XL = 3 units, LM = 4 units and MN = 5 units.
5. Join YN.
6. Through L and M, draw LB $\parallel$ YN and MC $\parallel$ YN, cutting XY at B and C, respectively.
7. With B as the centre and radius XB, draw an arc.
8. With C as the centre and radius CY, draw an arc cutting the previously drawn arc at A.
9. Join AB and AC.
Thus, $△$ABC is the required triangle.