Rectangle A has a length of 2x + 6 and a width of 3x. Rectangle B has a length of x + 2 and an area of 12 square units greater than Rectangle A’s area. What is a simplified expression for the width of Rectangle B?

Answer 1

Let's first find the area of Rectangle A:

Area of Rectangle A = length * width
Area of Rectangle A = (2x + 6)(3x)
Area of Rectangle A = 6x^2 + 18x

Now, the area of Rectangle B is 12 square units greater than the area of Rectangle A:

Area of Rectangle B = Area of Rectangle A + 12
(x + 2) * (width of Rectangle B) = 6x^2 + 18x + 12

Expanding the left side and simplifying, we get:

x(width of Rectangle B) + 2(width of Rectangle B) = 6x^2 + 18x + 12

Now, we know that the width of Rectangle A is 3x. So, the width of Rectangle B is:

3x + 2(width of Rectangle B) = 6x^2 + 18x + 12
2(width of Rectangle B) = 6x^2 + 15x + 12
width of Rectangle B = (6x^2 + 15x + 12)/2
width of Rectangle B = 3x^2 + 7.5x + 6

Therefore, a simplified expression for the width of Rectangle B is 3x^2 + 7.5x + 6.