Question

The combined area of a square and a rectangle is 33 square meters. The width of the rectangle is 1 meter more than the length of one side of the square and the length of the rectangle is 3 meters more

than its width.
a) Calculate the dimensions of the rectangle and its perimeter

b) Calculate the dimensions of the square.

Answer 1

4 m = width of the rectangle.

6 m = length of the rectangle

20 m = perimeter of rectangle

3 m = side of the square

Explanation:

Let s = length of side of square

s + 1 = width of rectangle

s + 3 = length of rectangle

Area of rectangle = (s + 1)(s + 3)

Area of square =
`s^(2)`

So, (s + 1)(s + 3) +
`s^(2)` = 33

`s^(2)` + 4s + 3 +
`s^(2)` = 33

2
`s^(2)` + 4s - 30 = 0

2(
`s^(2)` + 2s - 15) = 0

2(s + 5)(s - 3) = 0

s = -5 or s = 3

Length of a side cannot be negative, so -5 is ignored

3 m = side of the square

4 m = width of the rectangle

6 m = length of the rectangle

2(4) + 2(6) = 8 + 12 = 20 m = perimeter of rectangle