Question 263035
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*5}}}
{{{A[o] = 45}}}sq.ft.
Now let the width of the border be x, so the area of the inner flower bed can be expressed as:
{{{A[i] = (9-2x)(5-2x)}}}
{{{A[i] = 4x^2-28x+45}}} Subtract {{{A[i]}}} from {{{A[o]}}} and this is given as 24sq.ft.
{{{(45)-(4x^2-28x+45) = 24}}} Simplify.
{{{4x^2-28x+24 = 0}}} Divide through by 4 to simplify further.
{{{x^2-7x+6 = 0}}} Factor this.
{{{(x-1)(x-6) = 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.