SOLUTION: I can't find the right answer I don't think to this problem. A landscape architect has included a rectangular flower bed measuring 9 ft by 5 ft in her plans for a new building. Sh

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Question 263035: I can't find the right answer I don't think to this problem.
A landscape architect has included a rectangular flower bed measuring 9 ft by 5 ft in her plans for a new building. She wants to use two colors of flowers in the bed, one in the center and the other for a border of the same width on all four sides. If she has enough plants to cover 24 square feet for the border, how wide can the border be?
I use an equation of (5-2x)(9-2x)=24
I foil it, make it equal 0 to look like 4x^2-28x+21=0
The end result I get is 14 +/- 4 sqrt 7 over 21
That, if I am correct, comes out to a 0.585 ft border, which is too small.
I don't get it.
Thank you.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
First, find the area of the border by subtracting the area of the inner flower bed from the area of the entire garden.
The area of the garden (rectangular flower bed 9ft. by 5ft.) is:
A+=+9%2A5
A%5Bo%5D+=+45sq.ft.
Now let the width of the border be x, so the area of the inner flower bed can be expressed as:
A%5Bi%5D+=+%289-2x%29%285-2x%29
A%5Bi%5D+=+4x%5E2-28x%2B45 Subtract A%5Bi%5D from A%5Bo%5D and this is given as 24sq.ft.
%2845%29-%284x%5E2-28x%2B45%29+=+24 Simplify.
4x%5E2-28x%2B24+=+0 Divide through by 4 to simplify further.
x%5E2-7x%2B6+=+0 Factor this.
%28x-1%29%28x-6%29+=+0 so that...
x+=+1 or x+=+6 but the width, x, cannot be 6ft., so it must be 1ft.
The width of the border is 1 foot.