Question #19900

1 Answer
Sep 20, 2017

First of all lets change this worded question into a mathematical equation. Then The question says "twice the side of", and since "of" in worded questions implies multiplication, we have 2 times the side of the square as the length of the rectangle. Next we see "three units less," which implies subtraction, meaning we have 3 less of the square as the width of the rectangle. If we let #x# equal the length of the square, we get the rectangles dimensions as #2x# and #x-3#.

The area of a rectangle is the width times the length, and the area of a square is the length squared. If #x# equals the length of the square, we get

#(2x)(x-3)=x^2#. We then expand the equation to get

#2x^2-6x=x^2#. Now we subtract #x^2# from both sides to get

#x^2-6x=0#. We now factorize the equation using the rule #a^2+ab=a(a+b)#, to get

#x(x-6)=0#

From here we use the Null Factor Law, which states if #ab=0#,
#a=0# or #b=0#
If we let #a=x# in our equation of #x(x-6)=0#, we get
#x=0# for one of our values.
If we let #b=(x+6)# in our equation of #x(x-6)=0#, we get
#x-6=0#
#x=6# as our other value. Therefore
#x=0# or #x=6#

Since we are using measurement we must have a value greater then 0, which leaves us with #x=6#. In that case, the squares dimensions are #6*6#, with an area of 36, and the rectangles dimensions are #12*3#, with an area of 36.

I hope I helped!