Question

Question #19900

Answer 1

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!