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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) 16 in (c) 124in (D) 259 in

Wanahton is cooking a breadstick on a rectangular baking sheet measuring 912 9 \frac{1}{2} inches (in\mathrm{in} ) by 13 13 in\mathrm{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\mathrm{in} \newline(B) 16 16 in \mathrm{in} \newline(C) 124 124 in \mathrm{in} \newline(D) 259259 in\mathrm{in}

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Q. Wanahton is cooking a breadstick on a rectangular baking sheet measuring 912 9 \frac{1}{2} inches (in\mathrm{in} ) by 13 13 in\mathrm{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\mathrm{in} \newline(B) 16 16 in \mathrm{in} \newline(C) 124 124 in \mathrm{in} \newline(D) 259259 in\mathrm{in}
  1. Calculate Diagonal Formula: To find the length of the longest breadstick that can fit diagonally on 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 is d=length2+width2d = \sqrt{\text{length}^2 + \text{width}^2}.
  2. Convert Mixed Number: First, we 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\left(9 \times 2 + 1\right)/2 inches, which equals 192\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 + \left(\frac{19}{2}\right)^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: 169+3614=6764+3614=10374169 + \frac{361}{4} = \frac{676}{4} + \frac{361}{4} = \frac{1037}{4}
  6. Find Diagonal: Next, we take the square root of the sum to find the diagonal:\newlined=10374d = \sqrt{\frac{1037}{4}}\newlined=10374d = \frac{\sqrt{1037}}{\sqrt{4}}\newlined=10372d = \frac{\sqrt{1037}}{2}
  7. Approximate Square Root: Since we need to find the answer to the nearest inch, we can approximate the square root of 10371037. The square root of 10241024 is 3232, and since 10371037 is slightly larger than 10241024, the square root of 10371037 will be slightly larger than 3232.
  8. Divide Approximation: Dividing our approximation by 22 gives us:\newlined ≈\approx 32/232 / 2\newlined ≈\approx 1616
  9. Final Breadstick Length: Therefore, the longest breadstick Wanahton could bake to fit diagonally on the baking sheet is approximately 1616 inches to the nearest inch.

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