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

Explanation:

Square is x meters on each side.

Area of square = x²

Width of rectangle = x+1

Length of rectangle = x+4

Area of rectangle = (x+1)(x+4) = x²+5x+4

Combined area = 2x²+5x+4 = 33

2x²+5x-29 = 0

x = [-5+√(5²-4(2)(-29))]/[2(2)] = [-5 +√257]/4