Right Triangles practice questions

Right Triangles questions

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1. 1Right trianglesFoundation

   A right triangle has one leg of length 6 and a hypotenuse of length 10. Enter the length of the other leg.A right triangle has one leg of length 6 and a hypotenuse of length 10. Enter the length of the other leg.

   Student-produced response: write your own answer rather than choosing one.

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   Answer: 88

   By the Pythagorean theorem, 6² + b² = 10², so b² = 100 - 36 = 64 and b = 8.By the Pythagorean theorem, 6^2 + b^2 = 10^2, so b^2 = 100 - 36 = 64 and b = 8.

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2. 2Right trianglesFoundation

   A right triangle has legs of 7 and 24. What is its hypotenuse?A right triangle has legs of 7 and 24. What is its hypotenuse?

   • A3131
   • B2323
   • C2626
   • D2525
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   Answer: 2525

   7² + 24² = 49 + 576 = 625, and the square root of 625 is 25. Adding the legs gives 31; the hypotenuse is always less than that.7^2 + 24^2 = 49 + 576 = 625, and the square root of 625 is 25. Adding the legs gives 31; the hypotenuse is always less than that.

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3. 3Right trianglesFoundation

   A right triangle has legs of 15 and 20. What is its hypotenuse?A right triangle has legs of 15 and 20. What is its hypotenuse?

   • A3535
   • B3030
   • C2525
   • D2727
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   Answer: 2525

   15² + 20² = 225 + 400 = 625, and the square root of 625 is 25. This is the 3-4-5 triangle scaled by 5, which is worth recognizing on sight.15^2 + 20^2 = 225 + 400 = 625, and the square root of 625 is 25. This is the 3-4-5 triangle scaled by 5, which is worth recognizing on sight.

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4. 4Right trianglesStandard

   A right triangle has legs of length 5 and 12. What is the length of its hypotenuse?A right triangle has legs of length 5 and 12. What is the length of its hypotenuse?

   • A2525
   • B1717
   • C1515
   • D1313
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   Answer: 1313

   Use the Pythagorean theorem: 5² + 12² = 25 + 144 = 169. The square root of 169 is 13.Use the Pythagorean theorem: 5^2 + 12^2 = 25 + 144 = 169. The square root of 169 is 13.

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5. 5Right trianglesStandard

   A right triangle has legs of length 9 and 12. What is the length of its hypotenuse?A right triangle has legs of length 9 and 12. What is the length of its hypotenuse?

   • A2121
   • B1515
   • C1616
   • D1313
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   Answer: 1515

   9² + 12² = 81 + 144 = 225, and the square root of 225 is 15. Adding the legs gives 21, which is what the theorem exists to correct: the hypotenuse is always shorter than the two legs combined.9^2 + 12^2 = 81 + 144 = 225, and the square root of 225 is 15. Adding the legs gives 21, which is what the theorem exists to correct: the hypotenuse is always shorter than the two legs combined.

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6. 6Right trianglesStandard

   A ladder 13 m long leans against a vertical wall with its foot 5 m from the base of the wall. How far up the wall does the ladder reach?A ladder 13 m long leans against a vertical wall with its foot 5 m from the base of the wall. How far up the wall does the ladder reach?

   • A18 m18 m
   • B12 m12 m
   • C8 m8 m
   • Dthe square root of 194 mthe square root of 194 m
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   Answer: 12 m12 m

   The ladder is the hypotenuse, so the height is the square root of 13² - 5² = 169 - 25 = 144, which is 12 m. Adding the squares instead of subtracting them gives the square root of 194, the answer to a different arrangement.The ladder is the hypotenuse, so the height is the square root of 13^2 - 5^2 = 169 - 25 = 144, which is 12 m. Adding the squares instead of subtracting them gives the square root of 194, the answer to a different arrangement.

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7. 7Right trianglesStandard

   A right triangle has a hypotenuse of 25 and one leg of 7. Enter the length of the other leg.A right triangle has a hypotenuse of 25 and one leg of 7. Enter the length of the other leg.

   Student-produced response: write your own answer rather than choosing one.

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   Answer: 2424

   The other leg is the square root of 25² - 7² = 625 - 49 = 576, which is 24. Because the hypotenuse is given, the two squares are subtracted rather than added.The other leg is the square root of 25^2 - 7^2 = 625 - 49 = 576, which is 24. Because the hypotenuse is given, the two squares are subtracted rather than added.

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8. 8Right trianglesStandard

   A right triangle has legs of 20 and 21. Enter the length of its hypotenuse.A right triangle has legs of 20 and 21. Enter the length of its hypotenuse.

   Student-produced response: write your own answer rather than choosing one.

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   Answer: 2929

   20² + 21² = 400 + 441 = 841, and the square root of 841 is 29. The 20-21-29 triangle is one of the less familiar right triangles with whole-number sides.20^2 + 21^2 = 400 + 441 = 841, and the square root of 841 is 29. The 20-21-29 triangle is one of the less familiar right triangles with whole-number sides.

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9. 9Right trianglesChallenge

   A ladder 13 meters long leans against a wall with its foot 5 meters from the base. Enter how far up the wall it reaches, in meters.A ladder 13 meters long leans against a wall with its foot 5 meters from the base. Enter how far up the wall it reaches, in meters.

   Student-produced response: write your own answer rather than choosing one.

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   Answer: 1212

   The ladder is the hypotenuse, so 5² + h² = 13² gives h² = 169 - 25 = 144 and h = 12 meters.The ladder is the hypotenuse, so 5^2 + h^2 = 13^2 gives h^2 = 169 - 25 = 144 and h = 12 meters.

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10. 10Right trianglesChallenge

    A rectangle measures 9 by 12. Enter the length of its diagonal.A rectangle measures 9 by 12. Enter the length of its diagonal.

    Student-produced response: write your own answer rather than choosing one.

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    Answer: 1515

    The diagonal is the hypotenuse of a right triangle with legs 9 and 12: √81 + 144 = √225 = 15.The diagonal is the hypotenuse of a right triangle with legs 9 and 12: √(81 + 144) = √(225) = 15.

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