Question

If the length of a rectangle is seven feet less than the width and the perimeter is 78feet, find the width of the rectangle.

Answer 1

For this problem we know that the lenght of a rectangle is 7 ft less than the width who represent this equation:

$L=w-7$

With L the lenght and w the width. We also know that the perimeter of the rectangle is given by 78 ft and we need to find the width. The perimeter is defined as:

$P=2L+2w$

If we replace the condition of L=w-7 we got:

$P=2(w-7)+2w=2w-14+2w=4w-14$

Since we know the value of the perimeter we have:

$78=4w-14$

And we can solve for w and we got:

$w=\frac{78+14}{4}=23ft$

And the final answer for this case would be width =23ft