Question

The area, A, of a rectangle is 120x2 + 78x – 90, and the length, l, of the rectangle is 12x + 15. Which of the following gives the width, w, of the rectangle?

Answer 1

10x – 6

Explanation:

Answer 2

Width = 2(5x - 3)

Explanation:

The area A, of the rectangle, is given by 120x² + 78x - 90.

Now, the area can be expressed as 6(20x² + 13x - 15)

= 6(20x² + 25x - 12x -15)

= 6(4x + 5)(5x - 3).

Now, the length of the rectangle is given by (12x + 15) = 3(4x + 5)

So, the width of the rectangle =
`(Area)/(Length) = (6(4x + 5)(5x - 3))/(3(4x + 5)) = 2(5x - 3)` (Answer)