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

Answer:

Lengths of AB and BD could be 4 and 2.

Step-by-step 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.

$\frac{AB}{BD}=\frac{AC}{CE}$

so we can say, $\frac{AB}{AD}=\frac{AC}{AE}=\frac{BC}{DE}$

$\frac{AB}{AD}=\frac{BC}{DE}$

$\frac{AB}{AD} =\frac{2}{3}$

take resiprocal of both sides

$\frac{AD}{AB} =\frac{3}{2}$

subtract 1 form both sides

$\frac{AD}{AB} - 1 = \frac{3}{2}-1$

we get, $\frac{AD-AB}{AB} =\frac{3-2}{2}$

$\frac{BD}{AB} =\frac{1}{2}$

take resiprocal of both sides

$\frac{AB}{BD} =\frac{2}{1} =\frac{4}{2}$

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