Question

In the tile given below, length and breadth of rectangle DEBF are 40 m and 30 m respectively. If area of parallelogram ABCD is double that of the area of rectangle FDEB, then find AF.

• A. 30 m
• B. 40 m
• C. 60 m
• D. 80 m

Answer 1

The correct option is B 40 m

Given: Length of the rectangle = 40 m
Breadth of the rectangle = 30m

$\Rightarrow$ FB = DE = 40 m and DF = EB = 30 m

According to given condition,
area of parallelogram ABCD
= 2$\times$(area of rectangle FDEB)

$\Rightarrow$ base $\times$ height = 2 $\times$ (length $\times$ breadth)

$\Rightarrow$ AB $\times$ DF = 2 $\times$ (FB $\times$ DF)

$\Rightarrow$ AB $\times$ 30 = 2 $\times$ (40 $\times$ 30)

$\Rightarrow$ AB = 80 m

Now, base = AB = AF + FB

$\Rightarrow$ 80 = AF + FB

$\Rightarrow$ 80 = AF + 40

$\Rightarrow$ AF = 40 m

Hence, AF = 40 m