Question

In the given pentagon, ratio of area of trapezium ABCD to area of $△$BEC is 5:2 and AG = 6 cm, EF = 4 cm. Find the length of BC if AD = 6 cm.

• A. 6 cm
• B. 8 cm
• C. 9 cm
• D. 10 cm

Answer 1

The correct option is C 9 cm

Area of trapezium ABCD
= $\frac{1}{2}$$\times$(Sum of parallel sides)$\times$height
= $\frac{1}{2}$$\times$(AD+BC)$\times$AG
= $\frac{1}{2}$$\times$(6+BC)$\times$6
= 3$\times$(6+BC)

Area of $△$BEC = $\frac{1}{2}$$\times$base$\times$height
= $\frac{1}{2}$$\times$BC$\times$EF
= $\frac{1}{2}$$\times$BC$\times$4
= BC$\times$2

According to given condition,
$\frac{\text{area of ABCD}}{\text{area of}△\text{BEC}}=\frac{5}{2}\frac{\text{3}\times \text{(6+BC)}}{\text{BC}\times \text{2}}=\frac{5}{2}\frac{\text{6+BC}}{\text{BC}}=\frac{5}{3}3\times (6+BC)=5\times BC18+3\left(BC\right)=5\left(BC\right)18=2\left(BC\right)⟹BC=\frac{18}{2}=9\text{cm}$