Question

Rectangle A, (dimensions 6 by 10-x) has an area twice that of rectangle B (dimensions x by 2x+1) . What are the lengths and widths of both rectangles?

Answer 1

•Rectangle A: 6 by 7
•Rectangle B: 7 by 3

Explanation:

The area of a rectangle is given by `color(red)(A = l * w)`.

The area of rectangle A is `6(10 - x) = 60 - 6x`

The area of rectangle B is `x(2x + 1) = 2x^2 + x`

We are given that the area of rectangle A is twice the area of rectangle B. Therefore, we can write the following equation.

`60 - 6x = 2(2x^2 + x)`

`60 - 6x = 4x^2 + 2x`

`0 = 4x^2 + 8x - 60`

`0 = 4(x^2 + 2x - 15)`

`0 = (x + 5)(x - 3)`

`x = -5 and 3`

A negative answer for `x` is impossible, since we're talking about geometric shapes.

Therefore, the rectangles have the following measurements:

•Rectangle A: 6 by 7
•Rectangle B: 7 by 3

As you can see, rectangle A's area is twice the area of rectangle B, just as the problem indicated.

Hopefully this helps!