If the width (W) of the rectangle is 1 ft shorter than its length (L), then we can write the following equatiion:
W = L - 1
now since we know the formula for the area of a rectangle:
Area = length x width
Area = L * W
30 = L * (L - 1)
where we have substituted the width W using the expression in terms of the length in the first equation we wrote.
then we multiply as indicated:
30 = L^2 - L
and write all terms on one side of the equal sign:
L^2 - L - 30 = 0
we try solving this quadratic equation by grouping:
L^2 - 6 L + 5 L - 30 = 0
L (L - 6) + 5 (L - 6) = 0
(L - 6) * (L + 5) =0
then there are two possible solutions to make that product equal to zero:
L = 6
or
L= -5
We pick the POSITIVE answer since we are looking for a length
therefore the length of the rectangle is 6 feet.
Type a "6" in the blank of your question.