Quadratic Word Problems with Area

The original plan for Mr. Harris’s house is a rectangle that measures 40’ x 50’. Because of an increase in cost, the square footage of the house must be decreased to 1739 square feet. To do this, the length and width will be decreased by the same amount. By how much should they be decreased?

• 6 ft

• 43.5 ft

• 3 ft

• 1.5 ft

Joe wants to make a path around the outside of his garden, which is 50’ x 70’. If the path is of uniform width and the entire garden and path combined are to cover 4524 square feet, how wide should the path be?

• 4 feet

• 8 feet

• 58 feet

• 78 feet

• 20x²-20x-20

• 20x²-20

• 20x²+20x-20

• 20x²+20

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A farmer has 50 feet of fencing to enclose a rectangular garden with an area of exactly 144 square feet. The area of the garden can be modeled by the equation x(25 - x) -144  where x represents the length and width of the garden. Does he have enough fence to enclose the garden?

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There is a table with a width of 3 feet less than its length and an area of 10 square feet. Write and solve an equation to determine the length and width of the table. What is the perimeter of the rectangle?

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Calista is painting a new picture. The height (H) of the frame is 2 inches taller than it is wide (W). If the area of her picture is 35 in², which equation represents the area?

• 35 = (W)(2+W)

• 35 = (H)(2+H)

• W = 35 + 2

• H = 35 + 2

Calista is painting a new picture. The following equation represents the area. 35 = (W)(2 + W). Which equation is equivilant?

• W² - 2W - 35 = 0

• W² + 2W - 35 = 0

• W² + 2W + 35 = 0

• W² - 2W + 35 = 0