Question

Please help!

Find the ratio of the area of triangle XBY to the area of triangle ABC for the given measurements, if

XY = 2, AC = 3

a. 1/3
b. 2/3
c. 4/9

Answer 1

the answe is c

Explanation:

just did the lesson

Answer 2

(c)

Explanation:

Consider ΔXBY and ΔABC

∠XYB = ∠ACB [ Corresponding angles of parallel line (AC and XY) are equal]

∠XBY = ∠ABC (Common angles)

By AA similarity, ΔXBY
`\sim` ΔABC,

We know that the ratio of area of two similar triangles is the square of ratios of their sides.

Ratio of sides =
`(XY)/(AC)`

=
`(2)/(3)`

`(Area of \triangle XBY)/(Area of \triangle ABC)` =
`[(XY)/(AC)]^(2)`

=
`[(3)/(2)]^(2)`

=
`(4)/(9)`

Option (c) is correct