Question

Construct a ∆ABC whose perimeter is 14 cm and the sides are in the ratio 2 : 3 : 4.

Answer 1

Steps of construction:
1. Draw a line segment XY = 14 cm.
2. Construct an acute angle on XY and drawn in the downward direction
3. Starting from X , mark (2+3+4) = 9 equal distances along XZ.
4. Mark points L,M and N, such that XL = 2 units, LM = 3 units and MN = 4 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 centre and radius XB, draw an arc.
8. With C as centre and radius CY, draw an arc, cutting the previously drawn arcs at point A.
9. Join AB and AC.
$△$ABC, the required triangle, is thus drawn.