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BELL-WORK

Solve area and perimeter problems involving rectangular objects and find the lengths using algebraic expressions.

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BELL-WORK

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  1. BELL-WORK Factor 30g5 + 24g3h – 35g2h2 – 28h3 6g3(5g2 + 4h) – 7(5g2 + 4h) (5g2 + 4h)(6g3 – 7)

  2. Area Problems The area of a rectangular computer screen is 4x2 + 20x +16. The width of the screen is 2x + 8. What is the length of the screen? 4x2 + 20x +16 4[x2 + 5x + 4] 4[x2 + x + 4x + 4] 4[x(x + 1) + 4(x + 1)] 4(x + 4)(x + 1) Because the measure of 2x + 8 is given, we have to manipulate this answer: 2(x + 4)2(x + 1) (2x + 8)(2x + 1) Answer: 2x + 1

  3. Area Problems The area of a rectangular granite countertop is 12x2 + 10x – 12. The width of the countertop is 2x + 3. What is the length of the countertop? 12x2 + 10x –12 2[6x2 + 5x – 6] 2[6x2 + 9x – 4x – 6] 2[3x(2x + 3) – 2(2x + 3)] 2(2x + 3)(3x – 2) Because the measure of 2x + 3 is given, the other measure must be: 2(3x – 2) Answer: 6x – 4

  4. Area Problems The area of a rectangular book cover is 4x2 – 6x – 40. The width of the book cover is 2x – 8. What is the length of the book cover? 4x2 – 6x – 40 2[2x2 – 3x – 20] 2[2x2 + 5x – 8x – 20] 2[x(2x + 5) – 4(2x + 5)] 2(2x + 5)(x – 4) Because the measure of 2x – 8 is given, we have to manipulate this answer: (2x + 5)2(x – 4) (2x + 5)(2x – 8) Answer: 2x + 5

  5. Perimeter & Area Problems The function x2 + 13x – 48 represents the area of a rectangle. Give an expression for the perimeter of the rectangle. x2 + 13x – 48 x2 – 3x + 16x – 48 x(x – 3) + 16(x – 3) (x – 3)(x + 16) The rectangle must have dimensions (x – 3) and (x + 16) which means its perimeter is x – 3 + x + 16 + x – 3 + x + 16 4x + 26

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