<PRE><B>Question 186454</B>
how wide a uniform border should be left on a plot of land 7m by 11m to have
 a rectangular area of 45m^2 available for flowers?
:
Let x = width of the uniform border
then the dimensions of the flower area will be:
(7-2x) by (11-2x)
:
The area:
(7 - 2x) * (11 - 2x) = 45
FOIL
77 - 14x - 22x + 4x^2 = 45
Arrange as a quadratic equation
4x^2 - 36x + 77 - 45 = 0
4x^2 - 36x + 32 = 0
Simplify, divide by 4
x^2 - 9x + 8 = 0
Factor
(x-8)(x-1) = 0
Two solutions
x = 8
and
x = 1 meter; this is the solution that makes sense
:
:
Check by finding the area
(7-2) * (11-2) = 45</PRE>