Question

If in a rectangle, the length is increased and breadth is reduced each by 2 meters, then the area is reduced by 28 sq meters. If the length is reduced by 1 meter and breadth is increased by 2 meters, then the area is increased by 33 sq meters. Find the length and breadth of the rectangle.

• A. 23, 11
• B. 37, 26
• C. 21, 14
• D. 28, 18

Answer 1

The correct option is A

23, 11

Let the length and breadth of the rectangle be x and y respectively.

So the original area of the rectangle = xy

According to question, (x + 2)(y - 2) = xy-28 or xy - 2x + 2y - 4 = xy - 28 or 2x - 2y = 24 .....(i)

Next, (x - 1) (y + 2) = xy + 33 or xy + 2x - y - 2 = xy + 33 or 2x - y = 35 ....(ii)

Now we need to solve (i) and (ii)

Subtracting (i) from (ii) we get, y = 11

Substituting this value in (ii)

We get,

2x = 46
x = 23