So,
The sand box's area is 45 ft.
The length is 4 feet longer than the width.
We can solve by translating these sentences into mathematical form.
Let l represent length and w represent width.
First equation: lw = 45
Second equation: l = 4 + w
Substitute 4 + w for l in the first equation.
(4 + w)w = 45
Distribute
[tex] w^{2} + 4w = 45[/tex]
Subtract 45 from both sides
[tex] w^{2} + 4w - 45[/tex]
Factor
[tex](w + 9)(w -5) = w^{2} + 4w - 45[/tex]
Set both factors equal to zero.
w + 9 = 0
w - 5 = 0
Subtract 9 from both sides
w = -9
Add 5 to both sides
w = 5
We have to cross out -9 for the width, because, logically, it is impossible to have a negative width.
Substitute 5 for w in the second original equation.
l = 4 + (5)
l = 9
Check
5 * 9 = 45
45 = 45 This checks.
9 = 4 + 5
9 = 9 This also checks.
The length is 9 ft. and the width is 4 ft.
