Question

The area of rectangle RSTU is 36x2+25x−25. The length of the rectangle RSTU is 4x+5. Which expression describes the width of the rectangle RSTU?

Answer 1

Given:

The area of the rectangle RSTU =
`36x^2+25x-25`

Length of the rectangle RSTU =
`4x+5`

To find:

The width of the rectangle RSTU.

Explanation:

We have,

`36x^2+25x-25`

Splitting the middle term, we get

`=36x^2+45x-20x-25`

`=9x(4x+5)-5(4x+5)`

`=(4x+5)(9x-5)`

We know that, the area of a rectangle is

`Area=Length * width`

Area of rectangle is product of (4x+5) and (9x-5).

Since (4x+5) is the length of the rectangle, therefore, (9x-5) is the width of the rectangle RSTU.