Write An Algebraic Expression That Represents The Area Of Th

Question

Write An Algebraic Expression That Represents The Area Of The Flagb Write an algebraic expression that represents the area of the flag. b. They decided the area should be 260 square feet. What would the dimensions of the flag have to be? Use what you wrote in part a) to write an equation and solve it. c. They want to buy a fringe to fit exactly around the edges. Use your result from part b) to figure out how much fringe they need. d. They have exactly 90 square feet of the red material. Will they have enough red material for that part of the flag?

Dr. Jack HW Helper · Accepted Answer

The problem involves several steps centered around understanding the dimensions and materials needed for a rectangular flag. To approach this, we first need to define an algebraic expression for the area of the flag and then use the given area to determine its dimensions. Subsequently, calculations regarding peripheral fringe and red material will follow based on the earlier findings. Part a: Algebraic Expression for the Area Assuming the flag is rectangular, let its length be represented by $ l $ and its width by $ w $. The area $ A $ of a rectangle is given by the product of length and width: $$ A = l \times w $$ Therefore, the algebraic expression for the area of the flag is: $$ A = l \times w $$ If we have additional information relating $ l $ and $ w $, such as one dimension being a multiple or a sum involving a variable, this expression can be elaborated further. Part b: Finding Dimensions with a Given Area The problem states that the area should be 260 square feet. Using the algebraic expression for area: $$ l \times w = 260 $$ Suppose, for simplicity, that the length is twice the width, i.e., $$ l = 2w $$ Substitute into the area equation: $$ (2w) \times w = 260 $$ which simplifies to: $$ 2w^2 = 260 $$ Dividing both sides by 2: $$ w^2 = 130 $$ Taking the square root: $$ w = \sqrt{130} \approx 11.40 \text{ feet} $$ Then, the length: $$ l = 2w \approx 2 \times 11.40 = 22.80 \text{ feet} $$ Thus, the dimensions of the flag would be approximately 22.80 feet in length and 11.40 feet in width to achieve an area of 260 square feet with the assumed proportional relationship. Part c: Calculating the Fringe Needed The fringe fits exactly around the edges of the flag, which means calculating the perimeter: $$ P = 2(l + w) $$ Using the approximate dimensions: $$ P = 2(22.80 + 11.40) = 2(34.20) = 68.40 \text{ feet} $$ Therefore, the amount of fringe needed is approximately 68.40 feet. Part d: Red Material for the Red Part of the Flag Suppose the red material co

Write An Algebraic Expression That Represents The Area Of The Flagb

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