SOLUTION: The Lush Landscaping Company is involved in a project for the city. They are expanding the garden in front of the city hall by planting a border of flowers around it. The current d
Question 1077926: The Lush Landscaping Company is involved in a project for the city. They are expanding the garden in front of the city hall by planting a border of flowers around it. The current dimensions of the garden are 24 feet long by 16 feet wide. The border will have the same width around the entire garden. The flowers planted in the border will fill an area of 276 square feet.
#1.How can you find the area of the existing garden
#2.What are the variables in this situation?
#3.How can you represent the dimensions of the larger garden algebraically?
#4.How can you find the area of just the border?
#5.How does the area of 276 feet relate to this situation and your equation?
#6.Find the border area as a function of the border width x? Answer by jorel1380(3719) (Show Source):
You can put this solution on YOUR website! Let x be the width of the border. Then:
(24+2x)(16+2x)-276=(24)(16)[The dimensions of the garden]
384+80x+4x²-276=384
4x²+80x-276=0
x²+20x-69=0
(x+23)(x-3)=0
x=3 or -23
We get a positive value of 3 ft as the width of the border. ☺☺☺
