Question

Reggie currently has a square rug in his living room. He is moving soon and has determined that for his new living room, he will need a rug that has a width that is two feet shorter than his current rug and a length that is five feet longer than his current rug. Let x represents the side measure of Reggie's current rug, in feet. Determine the equation that represents the area, y, in square feet, of the rug needed for his new living room.
y = x2 + 3x - 10



y = x2 - 7x + 10



y = x2 - 3x - 10



y = x2 + 7x + 10

Answer 1

Answer:
y = x² + 3x - 10

Explanation:
Reggie's current rug has a square shape.
This means that:
length of rug = x ft
width of rug = x ft

For the new rug:
1- the length is 5 ft longer than the current rug. This means that:
new length = x + 5 ft
2- the width is 2 ft shorter than the current rug. This means that:
new width = x - 2 ft

The area of the new rug can be calculated as follows:
area of new rug = new length * new width
area of new rug = (x + 5)(x - 2)
area of new rug = x(x) - 2(x) + 5(x) - 5(2)
area of new rug = x² - 2x + 5x - 10
area of new rug = x² + 3x - 10 ft²

Hope this helps :)