Question

ABCD is a parallelogram such that AF = 7 cm, FB = 3 cm and EF = 4 cm, length FD = equals

Options

• `21/4 cm`

• `28/3 cm`

• `12/7 cm`

• 5.5 cm

Answer 1

`bb(28/3 cm)`

Explanation:

Given: FB = 3 cm, AF = 7 cm and EF = 4 cm.

From the diagram, E is a point on BC and line segment DF is drawn where F is on extended side AB.

In △FBE and △FAD:

Since AD || BC, ∠FBE = ∠FAD (corresponding angles)

And ∠FEB = ∠FDA (corresponding angles)

Thus, △FBE ∼ △FAD.

By similarity of △FBE ∼ △FAD, the ratios of corresponding sides are equal:

`(FB)/(FA) = (FE)/(FD)`

`3/7 = 4/(FD)`

3 × FD = 7 × 4

3 × FD = 28

`FD = 28/3 cm`

The length FD is `28/3 cm`.