Some days, Lacy runs one complete lap around a lake. Other days, she runs one complete lap around a park.

The following diagram shows the dimensions of the lake and park on a coordinate grid.

Coordinate values are in meters.
Which lap is longer, and how much longer?
Choose 1 answer:
(A) A lap around the park is longer by about $25 \mathrm{~m}$.
(B) A lap around the park is longer by about $13 \mathrm{~m}$.
(c) A lap around the lake is longer by about $25 \mathrm{~m}$.
(D) A lap around the lake is longer by about $13 \mathrm{~m}$.

Question

Some days, Lacy runs one complete lap around a lake. Other days, she runs one complete lap around a park.

The following diagram shows the dimensions of the lake and park on a coordinate grid.

Coordinate values are in meters.
Which lap is longer, and how much longer?
Choose 1 answer:
(A) A lap around the park is longer by about $25 \mathrm{~m}$.
(B) A lap around the park is longer by about $13 \mathrm{~m}$.
(c) A lap around the lake is longer by about $25 \mathrm{~m}$.
(D) A lap around the lake is longer by about $13 \mathrm{~m}$.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Calculate the circumference of the circle (lake) using the diameter: $C_{ ext{lake}} = \pi imes ext{diameter}$. ‖ ‖ step 2 ⋮ Substitute the diameter of 40 meters into the formula: $C_{ ext{lake}} = \pi imes 40 \approx 125.664 ext{ m}$. ‖ ‖ step 3 ⋮ Calculate the perimeter of the rhombus (park) using the length of one side: $P_{ ext{park}} = 4 imes ext{side length}$. ‖ ‖ step 4 ⋮ Substitute the side length of $\sqrt{2 imes 40^2}$ meters into the formula: $P_{ ext{park}} = 4 imes \sqrt{2 imes 40^2} \approx 226.274 ext{ m}$. ‖ ‖ step 5 ⋮ Compare the circumference of the lake with the perimeter of the park: $C_{ ext{lake}} \approx 125.664 ext{ m}$, $P_{ ext{park}} \approx 226.274 ext{ m}$. ‖ ‖ step 6 ⋮ Determine which lap is longer and by how much: $P_{ ext{park}} - C_{ ext{lake}} \approx 226.274 ext{ m} - 125.664 ext{ m} \approx 100.61 ext{ m}$. ‖ ∻1 Answer∻ ***B*** ∻Key Concept∻ ⚹Comparing Perimeters/Circumferences⚹ ∻Explanation∻ ⚹To determine which lap is longer, compare the perimeter of the rhombus to the circumference of the circle. The difference gives the length by which one lap is longer than the other.⚹◊What is the distance formula between two points in a coordinate⍭ Generate me a similar question◊

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