QuestionApril 20, 2025

Frankie wants to build a path from one corner of his yard to the opposite corner.His yard measures 20ft.times 32ft. What will be the length of his path to the nearest tenth of a foot? 21.5 ft 25.0 ft 32.6 ft 37.7 ft

Frankie wants to build a path from one corner of his yard to the opposite corner.His yard measures 20ft.times 32ft. What will be the length of his path to the nearest tenth of a foot? 21.5 ft 25.0 ft 32.6 ft 37.7 ft
Frankie wants to build a path from one corner of his yard to the opposite corner.His yard measures 20ft.times 32ft. What will be the length of his path to the nearest tenth of a foot? 21.5 ft 25.0 ft 32.6 ft 37.7 ft

Solution
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Answer

37.7 ft Explanation 1. Identify the path as a diagonal The path is the diagonal of a rectangle with dimensions 20 \text{ ft} \times 32 \text{ ft}. 2. Apply the Pythagorean theorem Use **c = \sqrt{a^2 + b^2}** where a = 20 \text{ ft} and b = 32 \text{ ft}. 3. Calculate the diagonal length c = \sqrt{20^2 + 32^2} = \sqrt{400 + 1024} = \sqrt{1424} 4. Compute the square root \sqrt{1424} \approx 37.7

Explanation

1. Identify the path as a diagonal<br /> The path is the diagonal of a rectangle with dimensions $20 \text{ ft} \times 32 \text{ ft}$.<br /><br />2. Apply the Pythagorean theorem<br /> Use **$c = \sqrt{a^2 + b^2}$** where $a = 20 \text{ ft}$ and $b = 32 \text{ ft}$.<br /><br />3. Calculate the diagonal length<br /> $c = \sqrt{20^2 + 32^2} = \sqrt{400 + 1024} = \sqrt{1424}$<br /><br />4. Compute the square root<br /> $\sqrt{1424} \approx 37.7$
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