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
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