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The area of a trapezium is 200 cm2. Its parallel sides ...

The area of a trapezium is 200 cm2. Its parallel sides are in the ratio 2 : 3 and the perpendicular distance between them is 16 cm. Find the length of each of the parallel sides

A.

10 cm and 15 cm

B.

8 cm and 12 cm

C.

6 cm and 9 cm

D.

12 cm and 18 cm

Correct answer is A

Area of trapezium = 12(a+b)h

12(a+b)×16=200

⇒ 8(a + b) = 200

⇒ a + b = 2008 = 25 -----(i)

⇒ a : b = 2 : 3

ab=23

⇒ 3a = 2b

⇒ a = 2b3 -------(ii)

Substitute 2b3 for a in equation (i)

2b3 + b = 25

 5b3 = 25

⇒ b = 25 ÷ 53=25×35=15cm

From equation (ii)

⇒ a = 2×153=2×5=10cm

∴ Lengths of each parallel sides are 10cm and 15cm