During a mountain expedition, Emek and Luna reached a damaged footbridge over a narrow ravine. Before choosing a safe crossing point, they examined a triangular support that formed a right triangle. The diagonal support measured 17 meters, while the vertical side measured 8 meters. The horizontal side represented the width of the ravine. Luna used the Pythagorean Theorem and reasoned that the missing length squared was 17 squared minus 8 squared. She calculated 289 - 64 = 225, so the ravine was 15 meters wide. Emek checked the result by confirming that 8 squared plus 15 squared equaled 17 squared. Their safety line could span up to 16 meters, giving them 1 meter beyond the required width. With the calculation verified, they selected that crossing point and prepared to cross safely.

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Challenge 1 of 4
Hint
The 17-meter diagonal is the hypotenuse. Start with 8 squared + w squared = 17 squared.
The diagonal support is 17 meters long, the vertical side is 8 meters, and the horizontal side is the unknown ravine width w. Which equation should Luna use to find w?
w squared = 17 squared + 8 squaredw squared = 17 squared - 8 squaredw squared = 8 squared - 17 squaredw = 17 - 8
Correct! Subtracting 8 squared from 17 squared isolates the square of the ravine width.
Not quite. The 17-meter side is the hypotenuse, so its square equals the sum of the squares of the two legs.
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Hint
Find 8 squared and 15 squared, then add the results.
Emek checks the 15-meter ravine width using 8 squared + 15 squared = 17 squared. What is the value of 8 squared + 15 squared?
Correct! 64 + 225 = 289, which also equals 17 squared.
Try again. Calculate 8 squared and 15 squared separately before adding.
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Hint
Use the Pythagorean Theorem with legs of 9 meters and 12 meters, then compare the diagonal with 16 meters.
At another possible crossing point, the ravine is 12 meters wide and a vertical support would be 9 meters high. The safety line can span up to 16 meters. If the safety line must follow the diagonal between the ends of these two perpendicular measurements, which conclusion is correct?
The diagonal is 21 meters, so the safety line is too short.The diagonal is 15 meters, so the safety line is long enough by 1 meter.The diagonal is 16 meters, so the safety line is exactly long enough.The diagonal is 12 meters, so the safety line is long enough by 4 meters.
Correct! The diagonal is 15 meters, so the 16-meter safety line is long enough by 1 meter.
Not quite. First find the diagonal from the 9-meter and 12-meter legs, then compare it with the safety line length.
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Kırık Dağ Köprüsü
TR
ARC_G08_GM_02_STORY_02
Kırık Dağ Köprüsü
The Broken Mountain Bridge
EN
ARC_G08_GM_02_STORY_02
The Broken Mountain Bridge