Question

Two rectangular pieces of cardboard have their lengths in the ratio 1:3, and their breadths in the ratio 2:7. The ratio of their areas would be.

• A. $3:14$
• B. $2:21$
• C. $4:9$

Answer 1

The correct option is B $2:21$

Given:
The ratio of the lengths of the two cardboard pieces = $1:3$
So, if the lengths of the two pieces are $l_1$ and $l_2$, then $l_1=l$ and $l_2=3l$.
Similarly, if the breadths of the two pieces are $b_1$ and $b_2$, then $b_1=2b$ and $b_2=7b$.
Area of a rectangle = length $\times$ breadth
The ratio of the areas of the two pieces is $\frac{A_1}{A_2}=\frac{l_1\times b_1}{l_2\times b_2}$
$⟹\frac{A_1}{A_2}=\frac{l\times 2b}{3l\times 7b}=\frac{2}{3\times 7}=\frac{2}{21}$
$\therefore$ The ratio of the areas is $2:21.$