Polynomial Expressions and Rectangle Problems
Explore polynomial expressions and solve rectangle problems where a painter creates artworks on canvases with different dimensions, adding frames around them. Find the original height and width of the rectangles based on given area measurements. Improve your math skills with these practical examples.
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Presentation Transcript
Rectangle Problem Keng creates a painting on a rectangular canvas with a width that is 4 inches longer than the height A. Write a polynomial expression, in simplified form, that represents the area of the canvas. B. 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. C. The area of the rectangle is 96 in2. Find the height and width of the original rectangle.
Answers A. h(h+4) = h2+ 4h B. (h + 3 + 3)(h + 4 + 3 + 3) = (h + 6)(h + 10) = h2+ 6h + 10h + 60 = h2+ 16h + 60
Part C Answer h(h + 4) = 96 h2+ 4h = 96 h2+ 4h 96 = 0 (h + 12) (h 8) = 0 h + 12 = 0 -12 -12 h = -12 Can t have negative height then h + 4=8+4=12 Therefore the height is 8 inches and the width is 12 inches h 8 = 0 +8 +8 h = 8
Rectangle Problem Keng creates a painting on a rectangular canvas with a width that is 5 inches longer than the height A. Write a polynomial expression, in simplified form, that represents the area of the canvas. B. 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. C. The area of the rectangle is 84 in2. Find the height and width of the original rectangle.
Answers A. h(h+5) = h2+ 5h B. (h + 2 + 2)(h + 5 + 2 + 2) = (h + 4)(h + 9) = h2+ 4h + 9h + 36 = h2+ 13h + 36
Part C Answer h(h + 5) =84 h2+ 5h = 84 h2+ 5h 84 = 0 (h + 12) (h 7) = 0 h + 12 = 0 -12 -12 h = -12 Can t have negative height then h + 5=7+5=12 Therefore the height is 7 inches and the width is 12 inches h 7 = 0 +7 +7 h = 7
Rectangle Problem Keng creates a painting on a rectangular canvas with a width that is 6 inches longer than the height A. Write a polynomial expression, in simplified form, that represents the area of the canvas. B. 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. C. The area of the rectangle is 27 in2. Find the height and width of the original rectangle.
Answers A. h(h+6) = h2+ 6h B. (h + 4 + 4)(h + 6 + 4 + 4) = (h + 8)(h + 14) = h2+ 8h + 14h + 112 = h2+ 22h + 112
Part C Answer h(h + 6) = 27 h2+ 6h = 27 h2+ 6h 27 = 0 (h + 9) (h 3) = 0 h + 9 = 0 -9 -9 h = -9 Can t have negative height then h + 6=3+6=9 Therefore the height is 3 inches and the width is 9 inches h 3 = 0 +3 +3 h = 3
