Question

The length of a rectangle is 6 cm more than its width. The area of the rectangle is 256 cm,superscript,2,baseline,. Let x represent the width of the rectangle in centimeters. Which equation represents the situation? Answer Options with 4 options A

. 6x,superscript,2,baseline, − 256 = 0 B
. 6x,superscript,2,baseline, + 256 = 0 C.
x ,superscript,2,baseline, − 6x + 256 = 0 D.
x ,superscript,2,baseline, + 6x − 256 = 0

Answer 1

The equation which represents the situation is:

`x^2+6x-256=0`

Explanation:

Let x represent the width of the rectangle in centimeters.

The length of a rectangle is 6 cm more than its width.

This means that the length of the rectangle is: x+6 cm.

Also, we know that the area of a rectangle is the product of the length and width of the rectangle.

Here, the area of the rectangle is 256 cm².

i.e.

`x(x+6)=256\\\\x^2+6x=256\\\\i.e.\\\\x^2+6x-256=0`