The width of a rectangle is 3 inches less than its length. The area of the rectangle is 340 square inches. What are the length and width of the rectangle?

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Answer 1 · 2016-04-19T01:00:38

Length and width are 20 and 17 inches, respectively.

First of all, let us consider #x# the length of the rectangle, and #y# its width. According to the initial statement:

#y = x-3#

Now, we know that the area of the rectangle is given by:

#A = x cdot y = x cdot (x-3) = x^2-3x#

and it is equal to:

#A = x^2-3x=340#

So we get the quadratic equation:

#x^2-3x-340=0#

Let us solve it:

#x = {-b pm sqrt{b^2-4ac}}/{2a}#

where #a, b, c# come from #ax^2+bx+c=0#. By substituting:

#x = {-(-3) pm sqrt{(-3)^2-4 cdot 1 cdot (-340)}}/{2 cdot 1} =#
#={3 pm sqrt{1369}}/{2} = {3 pm 37}/2#

We get two solutions:

#x_1 = {3 + 37}/2 = 20#
#x_2 = {3-37}/2 = -17#

As we are talking about inches, we must take the positive one.

So: