Question

There is a rectangle having sides as 20cm and 14 cm respectively. If the length is increased by 2cm and breadth by 3 cm. The increase in area is equal to

• A. $96c{m}^2$
• B. $94c{m}^2$
• C. $92c{m}^2$
• D. $98c{m}^2$

Answer 1

The correct option is B

$94c{m}^2$

Let ABCD be the given rectangle with AB = 20cm and BC = 14cm as shown.

Let length be increased by 2cm to B, such that BB' = 2cm

Let breadth be increased by 3cm to D, such that DD' = 3cm

Original area of rectangle $=AB\times BC$

$=20\times 14$

$=280c{m}^2$

Now area of rectangle AB'E'D' = $(20+2)(14+3)$

area AB'E'D' = $20\times 14+14\times 2+20\times 3+2\times 3$

We can observe that increase in the area is

$14\times 2+20\times 3+2\times 3$

$=28+60+6$

$=94c{m}^2$