Question

a square piece of paper has an area of $x^2$ square units. a rectangular strip with a width of 2 units and a length of $x$ units is cut off of the square piece of paper. the remaining piece of paper has an area of 120 square units. which equation can be used to solve for $x$, the side length of the origin square? $x^2 + 2x - 120 = 0$ $x^2 + 2x + 120 = 0$ $x^2 - 2x - 120 = 0$

Explanation:

Step1: Find area of the rectangle

The area of a rectangle is given by the formula \( \text{Area} = \text{length} \times \text{width} \). Here, the length is \( x \) units and the width is 2 units, so the area of the rectangular strip is \( 2\times x = 2x \) square units.

Step2: Set up the equation for remaining area

The area of the original square is \( x^2 \) square units. After cutting off the rectangular strip (area \( 2x \)), the remaining area is 120 square units. So, we can write the equation as:
\( x^2 - 2x = 120 \)

Step3: Rearrange the equation

Subtract 120 from both sides of the equation \( x^2 - 2x = 120 \) to get it in standard quadratic form \( ax^2 + bx + c = 0 \).
\( x^2 - 2x - 120 = 0 \)

Answer:

\( x^2 - 2x - 120 = 0 \) (the third option, assuming the options are presented in the order shown: the equation \( x^2 - 2x - 120 = 0 \))