Name: __________________ Sheet #15-­‐02 Topic: Quadratic Area Word Problems Aim: How do we solve area and perimeter word problems using quadratics? Do Now: If the area of a square is 36 ft2, what is the perimeter? #1) The perimeter of a rectangle is 20 meters and the #2) The perimeter of a rectangle is 44 inches. The area of area of the rectangle is 16 square meters. Find the the rectangle is 120 square inches. dimensions of the rectangle. #3) The perimeter of a rectangle is 40 feet and the area is #4) A 100-­‐foot fence is used to enclose a rectangular land 96 square feet. Determine the dimensions of the plot. If the area of the land plot is 456 square feet, which rectangle. equation can be used to determine the length (x) of the land plot? 1 x(100 – x) = 456 #5) A contractor has 48 meters of fencing that he is going to use to enclose the perimeter of a rectangular garden. The length of the garden is represented by L and the width is represented by W The area of the garden is 108 square meters. Determine, in meters, the dimensions of the garden. 2 2x + 2(100 – x) = 456 3 x(50 – x) = 456 4 2x + 2(50 – x) = 456 #6) Samantha is going to fence a rectangular pasture for her horse. The amount of fencing to be used is 32 feet. The fenced pasture will have an area of 63 square feet. Determine the length and width of the pasture. #7) A 4 inch by 6 inch photo is put into a picture frame with a border of constant width. If the area of the frame, including the picture, is 80 square inches, find an equation and solve for the width of the border. #8) A garden measuring 12 meters by 16 meters is to have a pedestrian pathway that is w meters wide installed all the way around it, increasing the total area to 285 square meters. Write an equation that can be used to determine the width, w, of the pathway. #9) A printer wants to put 54 square inches of text into a rectangle on an 8 by 11 sheet of paper. She wants the text to be surrounded by a border of constant width. Which equation could be used to find the width of the border (x)? (1) 2(8 -­‐ 2x) + 2(11 -­‐ 2x) = 54 (2) (8 -­‐ 2x) + (11 -­‐ 2x) = 54 (3) (8 -­‐ x)(11 -­‐ x) = 54 (4) (8 -­‐ 2x)(11 -­‐ 2x) = 54 Explain how this equation models the situation. Use this equation to solve for the width of the pathway.