MathIQO worksheet
Solve right-triangle problems using the Pythagorean theorem · Grade 9 · E1.5
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Date: ______________________
- 1
A right triangle has legs of 3 cm and 4 cm. Find the length of the hypotenuse, in cm.
Warm-upAnswer:
- 2
A right triangle has legs of 6 cm and 8 cm. Find the length of the hypotenuse, in cm.
Warm-upAnswer:
- 3
A right triangle has legs of 9 cm and 12 cm. Find the length of the hypotenuse, in cm.
Warm-upAnswer:
- 4
A right triangle has a hypotenuse of 29 cm and one leg of 20 cm. Find the length of the other leg, in cm.
On levelAnswer:
- 5
A right triangle has a hypotenuse of 26 cm and one leg of 10 cm. Find the length of the other leg, in cm.
On levelAnswer:
- 6
A right triangle has a hypotenuse of 5 cm and one leg of 3 cm. Find the length of the other leg, in cm.
On levelAnswer:
- 7
A ramp rises 72 cm over a horizontal run of 21 cm. How long is the sloped surface (the hypotenuse), in cm?
ChallengeAnswer:
- 8
A ramp rises 30 cm over a horizontal run of 16 cm. How long is the sloped surface (the hypotenuse), in cm?
ChallengeAnswer:
- 9
A ramp rises 72 cm over a horizontal run of 21 cm. How long is the sloped surface (the hypotenuse), in cm?
ChallengeAnswer:
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Worksheet code: eyJzIjoiZ2VvbWV0cnktcHl0aGFnb3JlYW4iLCJkIjpbMjExMjQ4MTc2Miw2MTQ4MzQ3ODQsNDAzMTg5ODkwLDE3OTIxMjIyODQsMTU3MzMyODczMyw2NTAzMDQwMzUsMTU0ODM1MzEwMSwyNTA2MTI5NjgsMTg5MzY2MjUzMV0sInYiOjF9.7be2f9e68859
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Answer key · Solve right-triangle problems using the Pythagorean theorem
- 1.5 — c² = 3² + 4² = 9 + 16 = 25, so c = 5 cm.
- 2.10 — c² = 6² + 8² = 36 + 64 = 100, so c = 10 cm.
- 3.15 — c² = 9² + 12² = 81 + 144 = 225, so c = 15 cm.
- 4.21 — leg² = 29² − 20² = 841 − 400 = 441, so the leg = 21 cm.
- 5.24 — leg² = 26² − 10² = 676 − 100 = 576, so the leg = 24 cm.
- 6.4 — leg² = 5² − 3² = 25 − 9 = 16, so the leg = 4 cm.
- 7.75 — length² = 21² + 72² = 5625, so the sloped surface is 75 cm.
- 8.34 — length² = 16² + 30² = 1156, so the sloped surface is 34 cm.
- 9.75 — length² = 21² + 72² = 5625, so the sloped surface is 75 cm.