Question

In the given figure, AX : XB = 3 : 5

Find:

1. the length of BC, if the length of XY is 18 cm.
2. the ratio between the areas of trapezium XBCY and triangle ABC.

Answer 1

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`