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#?

Question

Wyatt Anderson · Accepted Answer

#(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#

Allison Allen · Answer

The value of #x# is 5.

The following formula can be used to calculate a rectangle's area. #A=l*w# #l# stands for length or the longer side. #w# stands for width or the shorter side. We can now enter the provided values into the equation. #A=(x-2)*(x+8)# The simplest method of multiplying is to multiply these terms according to the order specified by the acronym FOIL, which stands for First Outside Inside Last. #A=x^2+8x-2x-16=x^2+6x-16# We can now enter the specified value for the area. #39=x^2+6x-16# The equation is then factored and all terms are moved to one side in order to simplify. #0=x^2+6x-55# At last, we factor the equation. To put it another way, we try to figure out the two things we multiplied together by doing a reverse-FOIL. #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.