Question

The perimeter of a rectangle is 36m. If its length is increased by 1m and the width is increased by 2m, its area will increase by 30m^2. Find the area of the original rectangle.

Answer 1

80 m^2

Explanation:

The given information lets you write two equations involving length (x) and width (y).

• 2(x +y) = 36 . . . . the perimeter is 36 m
• (x+1)(y+2) -xy = 30 . . . . increasing the length and width increases area

The second of these equations simplifies to another linear equation, giving a system of linear equations easily solved.

xy +y +2x + 2 -xy = 30

2x +y = 28 . . . . . . . subtract 2

Dividing the first equation by 2 gives

x +y = 18

and subtracting this from the above equation gives ...

(2x +y) -(x +y) = 28 -18

x = 10

Then

y = 18 -10 = 8

The area of the original rectangle is xy = 10·8 = 80 m^2.