Question

In the following figure, ABCD is a trapezium with AB$\parallel$DC. If AB=$9$ cm, DC= $18$ cm, CF= $13.5$ cm, AP= $6$ cm and BE= $15$ cm. Calculate EC

• A. EC= $12.5$ cm
• B. EC= $22.5$ cm
• C. EC= $20.5$ cm
• D. none of the above

Answer 1

The correct option is B EC= $22.5$ cm

In $△AEB$ and $△ECF$,
$\angle AEB=\angle CEF$ (vertically opposite angles)
$\angle ABE=\angle ECF$ (Alternate angles of parallel lines AB and CF)
$\angle BAE=\angle EFC$ (Alternate angles of parallel lines AB and CF)
Thus, $△AEB\sim △\angle FEC$ (AAA rule)
Hence, $\frac{AB}{CF}=\frac{BE}{EC}$
$\frac{9}{13.5}=\frac{15}{EC}$
$EC=\frac{15\times 13.5}{9}$
$EC=22.5$ cm