Question

Math

Posted 4 months ago

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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 $13 \mathrm{~m}$.
```

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Answer from Sia

Posted 4 months ago

Solution by Steps

step 2

Substitute the diameter of 40 meters into the formula: $C_{\text{lake}} = \pi \times 40 \approx 125.664 \text{ m}$

step 3

Calculate the perimeter of the rhombus (park) using the length of one side: $P_{\text{park}} = 4 \times \text{side length}$

step 4

Substitute the side length of $\sqrt{2 \times 40^2}$ meters into the formula: $P_{\text{park}} = 4 \times \sqrt{2 \times 40^2} \approx 226.274 \text{ m}$

step 5

Compare the circumference of the lake with the perimeter of the park: $C_{\text{lake}} \approx 125.664 \text{ m}$, $P_{\text{park}} \approx 226.274 \text{ m}$

step 6

Determine which lap is longer and by how much: $P_{\text{park}} - C_{\text{lake}} \approx 226.274 \text{ m} - 125.664 \text{ m} \approx 100.61 \text{ m}$

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.

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