While surveying a newly discovered meteor crater, Emek and Tara studied a map from an orbiting scanner. The crater's safe central region was shaped like a square with an area of 288 square meters. To find its side length, Tara wrote sqrt(288) and factored 288 as 144 times 2. This allowed her to simplify the length to 12sqrt(2) meters, or about 17.0 meters. The rover had two possible routes across the region. Route A was a straight 12sqrt(2)-meter path along one side of the safe zone, while Route B followed a marked path measuring 18.5 meters. Emek compared the distances and found that Route A was about 1.5 meters shorter. He also checked that its length matched the side of the square, so the entire path stayed within the scanner's safe boundary. With the distance confirmed, Emek and Tara programmed the rover to follow Route A and continued mapping the crater.

Challenges

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Challenge 1 of 5

Challenges

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Challenge 1 of 4
Hint
Factor 288 using a perfect-square factor, then take the square root of that factor.
Which sequence correctly shows why the side length of the 288-square-meter safe region can be written as 12sqrt(2) meters?
sqrt(288) = sqrt(144) + sqrt(2) = 12 + sqrt(2)sqrt(288) = sqrt(144 times 2) = sqrt(144)sqrt(2) = 12sqrt(2)sqrt(288) = sqrt(144 times 2) = 144sqrt(2)sqrt(288) = sqrt(288 / 2) = 12
Correct. Factoring out the perfect square 144 gives 12sqrt(2).
Not quite. Use 288 = 144 times 2 and simplify the square root of 144.
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Hint
First approximate one side using 12 times 1.4, then multiply by 3 and round to the nearest meter.
Suppose the rover must travel along three sides of the square safe region instead of one side. Each side is 12sqrt(2) meters. Using sqrt(2) approximately equal to 1.4, what is the approximate total distance, rounded to the nearest meter?
Correct. The three-side route is approximately 50 meters long.
Check the approximate length of one side, multiply it by 3, and then round to the nearest meter.
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Hint
Use a simple upper estimate for sqrt(2) that lets you compare 12sqrt(2) directly with 18.5.
Route A has an exact length of 12sqrt(2) meters, while Route B is 18.5 meters. Which comparison best explains why Route A is shorter without relying only on the story's decimal approximation?
Since sqrt(2) is less than 1.5, 12sqrt(2) is less than 18, and 18 is less than 18.5.Since sqrt(2) is greater than 2, 12sqrt(2) is greater than 24, so Route A is shorter.Since 12 is less than 18.5, multiplying 12 by sqrt(2) must make the result smaller.Since sqrt(2) is less than 2, 12sqrt(2) is less than 24, which proves it is less than 18.5.
Correct. Using sqrt(2) less than 1.5 shows that Route A is less than 18 meters and therefore shorter than Route B.
Not quite. The comparison must give an upper bound for Route A that is already below 18.5 meters.
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Meteor Kraterini Haritalamak
TR
ARC_G09_OPS_02_STORY_02
Meteor Kraterini Haritalamak
Mapping the Meteor Crater
EN
ARC_G09_OPS_02_STORY_02
Mapping the Meteor Crater