Question

There are two rectangles. Rectangle A has a width of 2x + 1 and a height of 2x, Rectangle B had a width of 3x and a height of x + 3. The areas of the rectangles are equal. Find the value of x. Show all your working.

Answer 1

Answer: x=7

Explanation:

Rectangle A Area:

`2x(2x+1)\\4x^2+2x`

Rectangle B Area:

`3x(x+3)\\3x^2+9x`

Now, you set them equal to each other:

`4x^2+2x = 3x^2+9x\\x^2=7x`

If x^2 = 7x, then x must equal 7.

(Basically, what you are saying is x*x=7x - if you divide by x, you get x=7)