Background $\newline$ Layout $\newline$ Theme $\newline$ Trans $\newline$ Question $131$ : $\newline$ To get from the pool to home, Fred can either take a bike path through the rectangular park or nide his bike along the two sides of the park. $\newline$ What measurement is cilosest to the distance of the bike path? $\newline$ A. $2.45 \mathrm{mi}$ $\newline$ C. $1.45 \mathrm{mi}$ $\newline$ B. $3.4 \mathrm{mi}$ $\newline$ D. $0.7 \mathrm{mi}$

Full solution

Q. Background

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Layout

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Theme

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Trans

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Question

131

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To get from the pool to home, Fred can either take a bike path through the rectangular park or nide his bike along the two sides of the park.

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What measurement is cilosest to the distance of the bike path?

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2.45 \mathrm{mi}

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1.45 \mathrm{mi}

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3.4 \mathrm{mi}

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0.7 \mathrm{mi}

Understand Park Layout: First, we need to understand the layout of the park and the paths Fred can take. Assume the park is a rectangle with length $l$ and width $w$ . Fred can either take a direct bike path through the park, which we assume is the diagonal, or ride around two sides of the rectangle.
Calculate Diagonal Length: Calculate the length of the diagonal using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Here, the hypotenuse is the diagonal $d$ of the rectangle, so $d = \sqrt{l^2 + w^2}$ .
Estimate Total Distance: We don't have the exact measurements of $l$ and $w$ , but we can estimate the diagonal distance by comparing it to the given options. Riding around the park involves traveling $l + w$ twice, so the total distance is $2(l + w)$ .
Compare Options: If the diagonal is shorter than traveling around the park, it should be less than $l + w$ . We need to find which option among A, B, C, D is less than $l + w$ and closest to a reasonable estimate of $\sqrt{l^2 + w^2}$ .
Choose Plausible Distance: Without specific values for $l$ and $w$ , we choose the smallest distance that is plausible for a diagonal, which would be less than the sum of the two sides but more than half of it. Comparing the options: A. $2$ . $45$ mi, B. $3$ . $4$ mi, C. $1$ . $45$ mi, D. $0$ . $7$ mi.