A parallelogram has height 45 cm and base 60 cm.a.find its area.b.what is the base and height of a parallelogram with twice the area?c.what is the base and height of a parallelogram with one-half the area?
Accepted Solution
A:
(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.