(a) Area of the parallelogram = 45 x 60 = 2700 cm²
Ratio of height : base = 45 : 60 = 3 : 4
When the area is doubled, area = 2700 x 2 = 5400 cm²
Let x be the factor,
(3x)(4x) = 5400
12x² = 5400
x² = 450
x =√450
x = 21.21
Height = 21.21x3 = 63.63
Base = 21.21x4 =84.84
(b) The base is 84.84 cm and the height is 63.63cm.
When the area is halved, the area is 2700 ÷ 2 = 1350 cm²
(3x)(4x) = 1350
12x² = 1350
x² = 112.5
x = √112.5
x = 10.61
Height = 10.61 x 3 = 31.83 cm
Base = 10.61 x 4 = 42.44 cm
C) The height is 31.83 cm and the base is 42.44 cm.
