While exploring a canyon, Emek and Luna reached two trail markers separated by steep ground. Their map showed that the marked paths formed a right angle: one path extended 9 meters along one canyon wall, while the other extended 12 meters along the adjoining wall. A direct route between the markers would form the hypotenuse of a right triangle. Using the Pythagorean Theorem, Luna calculated 9 squared plus 12 squared, giving 81 + 144 = 225. Emek found the square root of 225 and determined that the direct distance was 15 meters. Their climbing rope was 18 meters long, so it was 3 meters longer than the distance between the markers. After checking the measurements, they confirmed that the rope was long enough and safely prepared to use the shortcut.

Challenges

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Challenge 1 of 5

Challenges

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Challenge 1 of 4
Hint
The direct route is the hypotenuse of a right triangle. Use the Pythagorean Theorem.
The two canyon paths are 9 meters and 12 meters long and meet at a right angle. Which equation correctly finds the direct distance d between the trail markers?
d squared = 12 squared - 9 squaredd squared = 9 squared + 12 squaredd = 9 + 12d squared = 9 squared * 12 squared
Correct! The squares of the two leg lengths are added to find the square of the hypotenuse.
Not quite. Since the direct route is the hypotenuse, add the squares of the two perpendicular path lengths.
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Hint
Subtract the direct distance from the rope length.
The direct distance between the markers is 15 meters. Emek and Luna have an 18-meter rope. How many meters of rope will remain beyond the distance needed to reach directly between the markers?
Correct! The rope is 3 meters longer than the direct distance.
Try again. Find the difference between 18 meters and 15 meters.
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Hint
The 15-meter direct route is the hypotenuse. Subtract 9 squared from 15 squared, then find the square root.
Suppose another pair of canyon markers forms a right triangle with one leg measuring 9 meters and a direct route measuring 15 meters. How long is the other leg?
6 meters9 meters12 meters18 meters
Correct! The missing leg is 12 meters.
Not quite. Use the Pythagorean Theorem with 15 meters as the hypotenuse.
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Kanyondaki Kestirme Yol
TR
ARC_G08_GM_02_STORY_01
Kanyondaki Kestirme Yol
The Shortcut Across the Canyon
EN
ARC_G08_GM_02_STORY_01
The Shortcut Across the Canyon