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 xx equal the length of the square, we get the rectangles dimensions as 2x2x and x-3x3.

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

(2x)(x-3)=x^2(2x)(x3)=x2. We then expand the equation to get

2x^2-6x=x^22x26x=x2. Now we subtract x^2x2 from both sides to get

x^2-6x=0x26x=0. We now factorize the equation using the rule a^2+ab=a(a+b)a2+ab=a(a+b), to get

x(x-6)=0x(x6)=0

From here we use the Null Factor Law, which states if ab=0ab=0,
a=0a=0 or b=0b=0
If we let a=xa=x in our equation of x(x-6)=0x(x6)=0, we get
x=0x=0 for one of our values.
If we let b=(x+6)b=(x+6) in our equation of x(x-6)=0x(x6)=0, we get
x-6=0x6=0
x=6x=6 as our other value. Therefore
x=0x=0 or x=6x=6

Since we are using measurement we must have a value greater then 0, which leaves us with x=6x=6. In that case, the squares dimensions are 6*666, with an area of 36, and the rectangles dimensions are 12*3123, with an area of 36.

I hope I helped!