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Question

The height of a parallelogram is one-third of its base. If the area of the parallelogram is 108 cm2, find its base and height.

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Solution

Let the base of the parallelogram be x cm.
Then, the height of the parallelogram will be 13x cm.
It is given that the area of the parallelogram is 108 cm2.

Area of a parallelogram = Base × Height
∴ 108 cm2 = x × 13x
108 cm2 = 13x2
⇒ x2 = (108 × 3) cm2 = 324 cm2
⇒ x2 = (18 cm)2
⇒ x = 18 cm

∴ Base = x = 18 cm
Height = 13x = 13×18 cm
= 6 cm

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