SOLUTION: A garden 7 meter by 12 meter will be expanded by planting a border of flowers. The border will be of the same width around the entire garden and has an are of 92 meter^2

Algebra ->  Customizable Word Problem Solvers  -> Unit conversion -> SOLUTION: A garden 7 meter by 12 meter will be expanded by planting a border of flowers. The border will be of the same width around the entire garden and has an are of 92 meter^2      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 883511: A garden 7 meter by 12 meter will be expanded by planting a border of flowers. The border will be of the same width around the entire garden and has an are of 92 meter^2
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Try analyzing and solving this in general, since this is a very common type of rectangle area problem.

Let w= width of the original rectangle before adding the uniform additional width (x).
Let L = length
Let x = the additional width for the border.
Let A = the border area, which does not include the original rectangle (garden) area.

The unknown variable is x.

Garden Area: w*L
Flower Border Area: (w+2x)(L+2x)-wL
Knowing that this flower border is to be A, equation highlight_green%28%28w%2B2x%29%28L%2B2x%29-wL=A%29.

SOLVE FOR x SYMBOLICALLY FIRST.

FINISH VALUE FOR x SUBSTITUTING KNOWN AND GIVEN VALUES:
w=7
L=12
A=92