Question

BC parallel to DE. BC = 6, DE = 9 Which of the following could be the lengths of AB and BD respectively?

2 and 3
3 and 4.5
4 and 2
4 and 8

Answer 1

4 and 2

Explanation:

Answer 2

Lengths of AB and BD could be 4 and 2.

Explanation:

By using Basic Proportionality Theorem - If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.

`(AB)/(BD)=(AC)/(CE)`

so we can say,
`(AB)/(AD)=(AC)/(AE)=(BC)/(DE)`

`(AB)/(AD)=(BC)/(DE)`

`(AB)/(AD) =(2)/(3)`

take resiprocal of both sides

`(AD)/(AB) =(3)/(2)`

subtract 1 form both sides

`(AD)/(AB) - 1 = (3)/(2)-1`

we get,
`(AD-AB)/(AB) =(3-2)/(2)`

`(BD)/(AB) =(1)/(2)`

take resiprocal of both sides

`(AB)/(BD) =(2)/(1) =(4)/(2)`

Thus, lengths of AB and BD could be 4 and 2.