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Raggedy Rugs is holding their annual rug blowout sale this weekend! Since rugs will only be $6\$6 per square foot, Katie is going to get a new rug for her apartment. The rug is shaped like a rectangle with a width of 88 feet and a diagonal length of 1717 feet. How much will the rug cost?\newline$\$____

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Q. Raggedy Rugs is holding their annual rug blowout sale this weekend! Since rugs will only be $6\$6 per square foot, Katie is going to get a new rug for her apartment. The rug is shaped like a rectangle with a width of 88 feet and a diagonal length of 1717 feet. How much will the rug cost?\newline$\$____
  1. Calculate Rug Length: Calculate the length of the rug using the Pythagorean theorem. Given the diagonal (1717 feet) and the width (88 feet), we need to find the length.\newline82+length2=172 8^2 + \text{length}^2 = 17^2 \newline64+length2=289 64 + \text{length}^2 = 289 \newlinelength2=225 \text{length}^2 = 225 \newlinelength=15 feet \text{length} = 15 \text{ feet}
  2. Calculate Rug Area: Calculate the area of the rug using the dimensions found. The rug is a rectangle with a width of 88 feet and a length of 1515 feet.\newlineArea=width×length \text{Area} = \text{width} \times \text{length} \newlineArea=8×15 \text{Area} = 8 \times 15 \newlineArea=120 square feet \text{Area} = 120 \text{ square feet}
  3. Calculate Rug Cost: Calculate the cost of the rug by multiplying the area by the price per square foot. The price per square foot is $\(6\).\(\newline\)\[ \text{Cost} = \text{Area} \times \text{price per square foot} \]\(\newline\)\[ \text{Cost} = 120 \times 6 \]\(\newline\)\[ \text{Cost} = 720 \text{ dollars} \]

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