Question

a rectangle is drawn so that the width is 1 foot shorter than the length. the area of a rectangle is 30 square feet. find the length of the rectangle.___feet

Answer 1

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.