Question

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

Answer 1

Opposite sides of a rectangle are equal. Let x = length and y = width.
Knowing that the area of a rectangle is length times width and that the perimeter is 2x + 2y,
P = 36 = 2x+ 2y
xy + 30 = (x + 1)(y + 2) original area is 30 less than the new area,
xy + 30 = xy + 2x + y + 2
30 = 2x + y + 2
28 = 2x + y
36 = 2x + 2y subtract the two equations to get
-8 = -y
y = 8

28 = 2x + 8
2x = 20
x = 10

Checking this, perimeter of a 10x8 rectangle is 20 + 16 = 36.
Area would be 80.
Adding one to the length and two to the width, the rectangle becomes a 11x10 rectangle. Area of that would be 110.

Since 110 - 80 is 30, all of the constraints are satisfied; the answer is 80m²