ABCD is a parallelogram in which the line through A and F meets BC ...

Question

ABCD is a parallelogram in which the line through A and F meets BC produced at E, with $AF = 7$ cm, $FB = 3$ cm and $EF = 4$ cm (F lies on diagonal DB). Length FD equals

Accepted Answer

Step 1: In $	riangle AFD$ and $	riangle EFB$:
$\angle AFD=\angle EFB$ (vertically opposite angles)
$\angle ADF=\angle EBF$ (alternate angles, since $AD\parallel BC$)
Step 2: So $	riangle AFD\sim	riangle EFB$ (AA similarity).
Step 3: Corresponding sides are proportional:
$$\frac{AF}{EF}=\frac{FD}{FB}$$
Step 4: $$\frac{7}{4}=\frac{FD}{3}\ \Rightarrow\ FD=\frac{21}{4}	ext{ cm}$$
Answer: (A) $\dfrac{21}{4}$ cm

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