Question

1. jessica ran the width of a field, a distance of 55 meters. then she ran the length of the field, a distance of 76 meters. how far apart are opposite corners of the field?

meters
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Explanation:

Step1: Identify the problem type

This is a right triangle problem where the width and length of the field are the two legs, and the distance between opposite corners (the diagonal) is the hypotenuse. We can use the Pythagorean theorem, \( c = \sqrt{a^2 + b^2} \), where \( a = 55 \) meters (width) and \( b = 76 \) meters (length), and \( c \) is the diagonal.

Step2: Calculate \( a^2 \) and \( b^2 \)

First, calculate \( 55^2 \): \( 55^2 = 55 \times 55 = 3025 \)
Then, calculate \( 76^2 \): \( 76^2 = 76 \times 76 = 5776 \)

Step3: Sum the squares

Add the two results: \( 3025 + 5776 = 8801 \)

Step4: Take the square root

Find the square root of 8801: \( c = \sqrt{8801} \approx 93.81 \) (rounded to two decimal places) or if we consider the exact value, but typically we use the approximate. Wait, let's check the calculation again. Wait, 55 squared is 3025, 76 squared: 70 squared is 4900, 6 squared is 36, and 2706=840, so (70+6)^2=4900+840+36=5776. Then 3025+5776=8801. Now, what's the square root of 8801? Let's see, 94 squared is 8836, which is more than 8801. 93 squared is 8649. So 93.8 squared: 93^2=8649, 0.8^2=0.64, 2930.8=148.8, so (93+0.8)^2=8649+148.8+0.64=8798.44. Close to 8801. The difference is 8801 - 8798.44 = 2.56. So 93.8 + (2.56)/(2*93.8) ≈ 93.8 + 0.0136 ≈ 93.81. So approximately 94 meters (if we round to the nearest whole number) or more precisely ~93.8 meters. Wait, maybe I made a mistake in the numbers. Wait, the problem says "55 meters" (width) and "76 meters" (length)? Wait, the original text: "Jess ran the width of a field, a distance of 55 meters. Then she ran the length of the field, a distance of 76 meters. How far apart are opposite corners of the field?" So yes, width = 55, length = 76. So diagonal is sqrt(55² + 76²) = sqrt(3025 + 5776) = sqrt(8801) ≈ 93.81 meters, which is approximately 94 meters.

Answer:

Approximately \(\boxed{94}\) meters (or more precisely \(\approx 93.8\) meters, but likely rounded to whole number as 94).