a square piece of paper has an area of $x^{2}$ square units. a rectangular strip with a width of 2 units and…

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 original square? $x^{2}-2x - 120 = 0$ $x^{2}+2x - 120 = 0$ $x^{2}-2x + 120 = 0$ $x^{2}+2x + 120 = 0$

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 original square? $x^{2}-2x - 120 = 0$ $x^{2}+2x - 120 = 0$ $x^{2}-2x + 120 = 0$ $x^{2}+2x + 120 = 0$

Answer

Explanation:

Step1: Find area of the rectangular strip

The area of a rectangle is length times width. Here, width = 2 units and length = $x$ units, so the area of the rectangular strip is $2x$ square units.

Step2: Set up the equation based on the given areas

The area of the original square is $x^{2}$ square units. After cutting off the rectangular - strip, the remaining area is 120 square units. So, the area of the original square minus the area of the rectangular strip equals the remaining area. That is $x^{2}-2x = 120$.

Step3: Rearrange the equation

Subtract 120 from both sides of the equation $x^{2}-2x = 120$ to get it in standard quadratic form $x^{2}-2x - 120=0$.

Answer:

$x^{2}-2x - 120 = 0$