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ABCD is a parallelogram, DE is perpendicular to AB and DF is perpendicular to BC. If AB = 20 cm, BC = 10 cm and DF = 9 cm, then find DE.

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4.5 cm

10.5 cm

6.7 cm

9 cm

answer is B.

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Detailed Solution

Given, DF is perpendicular to BC

Taking BC as a base, BC = 10 cm

Height DF = 9 cm

Area of parallelogram ABCD = base x height

= 10 x 9

= 90 cm² ... (eq. 1)

DE is perpendicular to AB

Taking AB as a base, AB = 20 cm

height is DE

Area of parallelogram ABCD = base x height

= 20 x DE ... (eq. 2)

From eq. 1 and eq. 2,

90 = 20 x DE

DE = $\frac{90}{20}$ = 4.5 cm

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