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A jogger running around a rectangular park takes a shortcut back to her car by jogging from one corner of the park to the diagonally opposite corner. If the park is $60\,\text{yards}$ by $45\,\text{yards}$ , how far is the shortcut? $\newline$ $\_\_\_\_\_$ yards

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Pythagorean theorem

Full solution

Q. A jogger running around a rectangular park takes a shortcut back to her car by jogging from one corner of the park to the diagonally opposite corner. If the park is

60\,\text{yards}

by

45\,\text{yards}

, how far is the shortcut?

\newline

\_\_\_\_\_

yards

Identify sides as legs: Identify the lengths of the rectangle sides as legs of a right triangle, where the shortcut is the hypotenuse.
Use Pythagorean Theorem: We know: $\newline$ Length of the park: $60$ yards $\newline$ Width of the park: $45$ yards $\newline$ Use the Pythagorean Theorem to find the hypotenuse (shortcut).
Apply Pythagorean Theorem: Apply the Pythagorean Theorem: $a^2 + b^2 = c^2$ $60^2 + 45^2 = c^2$
Calculate squares: Calculate the squares of the lengths: $\newline$ $60^2 = 3600$ $\newline$ $45^2 = 2025$ $\newline$ $3600 + 2025 = c^2$
Add squares: Add the squares of the lengths: $3600 + 2025 = 5625$ $c^2 = 5625$
Find square root: Find the square root of $c^2$ to get the length of the hypotenuse: $\newline$ $\sqrt{c^2} = \sqrt{5625}$ $\newline$ $c = 75$

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