Question

If the area around the vegetable garden is of uniform width (labeled with x) and the dimensions of the vegetable garden is 45 feet by 20 feet, what expression represents the area of the flower garden?
Make sure to show all of your steps in your answer, including the area of the vegetable garden and the area of the entire garden.

Answer 1

Area of Rectangle = Width × Length

Vegetable Garden
Width = 20
Length = 45
Area of Vegetable Garden = 20×45=900 Sq ft

Area of Entire Garden = Width × Length
Width = 20 + 2x
Length = 45 + 2x
Area = (20 + 2x)(45 + 2x)
(2x + 20)(2x + 45)
4x^2 + 90x + 45x + 900
Area of Entire Garden = 4x^2 + 135x + 900

Area of Flower Garden = Area of Entire Garden - Area of Vegetable Garden

(4x^2 + 135x + 900) - (20 × 45)
4x^2 + 135x + 900 - 900
Area of Flower Garden = 4x^2 + 135x