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Question
In the adjoining figure. BC is parallel to DE, area of ΔABC = 25 sq cm, area of trapezium BCED = 24 sq cm, DE = 14 cm. Calculate the length of BC.
Solution
Given: Area of ΔABC = 25 cm2
Area of trapezium BCED = 24 cm2
and DE = 14 cm
∴ Area of ΔADE = area of ΔABC - area of trap. BCED
= 25 - 24
= 1 cm2
∵ ΔABC ∼ ΔADE
∴ `"Area of (ΔABC)"/"Area of (ΔADE)" = "BC"^2/"DE"^2`
`(25)/(1) = "BC"^2/14^2`
`"BC"/(14) = (5)/(1)`
BC = 5 x 14
= 70 cm.
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