If the area of a rectangle is 39 square feet and it has sides of #x-2# and #x+8#, what is the value of #x#?

2 Answers
May 3, 2018

#(x-2)(x+8)=39#

#x^2 +6x - 16 - 39 = 0#

#x^2 +6 x - 55 = 0#

#(x+11)(x-5) = 0#

#x=5 quad# We can skip #x=-11# which gives negative sides.

Check: #(5-2)(5+8)=(3)(13)=39 quad sqrt#

May 3, 2018

The value of #x# is 5.

Explanation:

The area of a rectangle can be determined by the following formula.

#A=l*w#

#l# stands for length or the longer side.
#w# stands for width or the shorter side.

Now, we can plug the values we are given into the equation.

#A=(x-2)*(x+8)#

The easiest way to multiply is to follow the acronym FOIL , which stands for First Outside Inside Last, and dictates the order in which you multiply these terms.

#A=x^2+8x-2x-16=x^2+6x-16#

Now, we can plug in the given value for the area.

#39=x^2+6x-16#

Next, we simplify by moving all terms to one side and factor the equation.

#0=x^2+6x-55#

Finally, we factor the equation. This means we reverse-FOIL, trying to determine the two things that we multiplied together.

#0=(x-5)*(x+11)#

If the equation ultimately equals zero, either #(x-5)# or #(x+11)# or both equal zero. Therefore, we set each equal to zero to find the value of #x#.

#x-5=0#
#x=5#

#x+11=0#
#x=-11#

Since #x# is a length, we know it cannot be negative. Thus, we can conclude that it equals 5.