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Wanahton is cooking a breadstick on a rectangular baking sheet measuring 9(1)/(2) inches (in) by 13 in. Assuming the breadstick width is negligible, what is the longest breadstick Wanahton could bake by fitting it straight along the diagonal and within the baking sheet to the nearest inch? Choose 1 answer: (A) 13 in (B) 16in (C) 124in (D) 259in

Wanahton is cooking a breadstick on a rectangular baking sheet measuring 9129\frac{1}{2} inches (in) by 1313 in. Assuming the breadstick width is negligible, what is the longest breadstick Wanahton could bake by fitting it straight along the diagonal and within the baking sheet to the nearest inch?\newlineChoose 11 answer:\newline(A) 1313 in\newline(B) 1616 in\newline(C) 124124 in\newline(D) 259259 in

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Q. Wanahton is cooking a breadstick on a rectangular baking sheet measuring 9129\frac{1}{2} inches (in) by 1313 in. Assuming the breadstick width is negligible, what is the longest breadstick Wanahton could bake by fitting it straight along the diagonal and within the baking sheet to the nearest inch?\newlineChoose 11 answer:\newline(A) 1313 in\newline(B) 1616 in\newline(C) 124124 in\newline(D) 259259 in
  1. Calculate Diagonal Formula: To find the length of the longest breadstick that can fit diagonally within the baking sheet, we need to calculate the diagonal of the rectangle using the Pythagorean theorem. The formula for the diagonal dd of a rectangle with length ll and width ww is d=l2+w2d = \sqrt{l^2 + w^2}.
  2. Convert to Improper Fraction: First, we need to convert the mixed number 9(12)9\left(\frac{1}{2}\right) inches to an improper fraction to make the calculation easier. 9(12)9\left(\frac{1}{2}\right) inches is the same as (9×2+1)/2=192\left(9 \times 2 + 1\right)/2 = \frac{19}{2} inches.
  3. Apply Pythagorean Theorem: Now we can apply the Pythagorean theorem. The length of the rectangle is 1313 inches, and the width is 192\frac{19}{2} inches. So, the diagonal dd is calculated as follows:\newlined=(13)2+(192)2d = \sqrt{(13)^2 + (\frac{19}{2})^2}
  4. Calculate Squares: Let's calculate the squares of the length and width:\newline132=16913^2 = 169\newline(192)2=(19222)=3614(\frac{19}{2})^2 = (\frac{19^2}{2^2}) = \frac{361}{4}
  5. Add Squares: Now, we add the squares of the length and width to find the square of the diagonal: 169+3614=6764+3614=10374169 + \frac{361}{4} = \frac{676}{4} + \frac{361}{4} = \frac{1037}{4}
  6. Find Square Root: Next, we take the square root of 1037/41037/4 to find the length of the diagonal:\newlined=1037/4=1037/4d = \sqrt{1037/4} = \sqrt{1037} / \sqrt{4}
  7. Estimate Square Root: Since we don't have a perfect square under the square root, we can estimate the square root of 10371037. We know that 322=102432^2 = 1024 and 332=108933^2 = 1089. So, 1037\sqrt{1037} is between 3232 and 3333.
  8. Estimate Diagonal Length: Given that 1037\sqrt{1037} is closer to 3232 than to 3333 and 4=2\sqrt{4} = 2, we can estimate the diagonal to be slightly more than 322\frac{32}{2} inches.
  9. Round to Nearest Inch: Dividing 3232 by 22 gives us 1616, so the diagonal is slightly more than 1616 inches. Since we need to round to the nearest inch, the longest breadstick Wanahton could bake to fit diagonally within the baking sheet is approximately 1616 inches.

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