Constructed Responses

Rectangle Problem Keng creates a painting on a rectangular canvas with a width that is 4 inches longer than the height Write a polynomial expression, in simplified form, that represents the area of the canvas. Keng adds a 3-inch-wide frame around all sides of his canvas. Write a polynomial expression, in simplified form, that represents the total area of the canvas and the frame. The area of the rectangle is 96 in2. Find the height and width of the original rectangle.

Answers h(h+4) = h2 + 4h (h + 3 + 3)(h + 4 + 3 + 3) = (h + 6)(h + 10)

Part C Answer h(h + 4) = 96 h2 + 4h = 96 h2 + 4h – 96 = 0 -12 -12 +8 +8 h = -12 h = 8 Can’t have negative height then h + 4=8+4=12 Therefore the height is 8 inches and the width is 12 inches

Rectangle Problem Keng creates a painting on a rectangular canvas with a width that is 5 inches longer than the height Write a polynomial expression, in simplified form, that represents the area of the canvas. Keng adds a 2-inch-wide frame around all sides of his canvas. Write a polynomial expression, in simplified form, that represents the total area of the canvas and the frame. The area of the rectangle is 84 in2. Find the height and width of the original rectangle.

Answers h(h+5) = h2 + 5h (h + 2 + 2)(h + 5 + 2 + 2) = (h + 4)(h + 9)

Part C Answer h(h + 5) =84 h2 + 5h = 84 h2 + 5h – 84 = 0 -12 -12 +7 +7 h = -12 h = 7 Can’t have negative height then h + 5=7+5=12 Therefore the height is 7 inches and the width is 12 inches

Rectangle Problem Keng creates a painting on a rectangular canvas with a width that is 6 inches longer than the height Write a polynomial expression, in simplified form, that represents the area of the canvas. Keng adds a 4-inch-wide frame around all sides of his canvas. Write a polynomial expression, in simplified form, that represents the total area of the canvas and the frame. The area of the rectangle is 27 in2. Find the height and width of the original rectangle.

Answers h(h+6) = h2 + 6h (h + 4 + 4)(h + 6 + 4 + 4) = (h + 8)(h + 14)

Part C Answer h(h + 6) = 27 h2 + 6h = 27 h2 + 6h – 27 = 0 -9 -9 +3 +3 h = -9 h = 3 Can’t have negative height then h + 6=3+6=9 Therefore the height is 3 inches and the width is 9 inches