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प्रश्न
In the given figure, AX : XB = 3 : 5
Find:
- the length of BC, if the length of XY is 18 cm.
- the ratio between the areas of trapezium XBCY and triangle ABC.
उत्तर
Given,
`(AX)/(XB) = 3/5 => (AX)/(AB) = 3/8` ...(1)
i. In ΔAXY and ΔABC,
As XY || BC, Corresponding angles are equal
∠AXY = ∠ABC
∠AYX = ∠ACB
ΔAXY ~ ΔABC
`=> (AX)/(AB) = (XY)/(BC)`
`=> 3/8 = 18/(BC)`
`=>` BC = 48 cm
ii. `"Area of ΔAXY"/"Area of ΔABC" = (AX^2)/(AB^2) = 9/64`
`"Area of ΔABC – Area of ΔAXY"/"Area of ΔABC" = (64 - 9)/64 = 55/64`
`"Area of trapezium XBCY"/"Area of ΔABC" = 55/64`
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