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 20 cm and 21 cm. Find the length of the hypotenuse, in cm.
Warm-upAnswer:
- 2
A right triangle has legs of 7 cm and 24 cm. Find the length of the hypotenuse, in cm.
Warm-upAnswer:
- 3
A right triangle has legs of 6 cm and 8 cm. Find the length of the hypotenuse, in cm.
Warm-upAnswer:
- 4
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:
- 5
A right triangle has a hypotenuse of 25 cm and one leg of 7 cm. Find the length of the other leg, in cm.
On levelAnswer:
- 6
A right triangle has a hypotenuse of 15 cm and one leg of 9 cm. Find the length of the other leg, in cm.
On levelAnswer:
- 7
A ramp rises 48 cm over a horizontal run of 20 cm. How long is the sloped surface (the hypotenuse), in cm?
ChallengeAnswer:
- 8
A ramp rises 8 cm over a horizontal run of 6 cm. How long is the sloped surface (the hypotenuse), in cm?
ChallengeAnswer:
- 9
A ramp rises 30 cm over a horizontal run of 16 cm. How long is the sloped surface (the hypotenuse), in cm?
ChallengeAnswer:
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Worksheet code: eyJzIjoiZ2VvbWV0cnktcHl0aGFnb3JlYW4iLCJkIjpbNjY2NDMxNTY2LDE4MDU0NTk2OTYsNDg4NTc0ODgyLDY2MzYzNDA4MSwxNzA2MDc2MDkzLDE1MTc2MjI1NzUsMTc1NTczMTg4NSwyMDY1NjIxOTA2LDIwMjY5MTI5ODFdLCJ2IjoxfQ.8c6ec73071cf
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Answer key · Solve right-triangle problems using the Pythagorean theorem
- 1.29 — c² = 20² + 21² = 400 + 441 = 841, so c = 29 cm.
- 2.25 — c² = 7² + 24² = 49 + 576 = 625, so c = 25 cm.
- 3.10 — c² = 6² + 8² = 36 + 64 = 100, so c = 10 cm.
- 4.24 — leg² = 26² − 10² = 676 − 100 = 576, so the leg = 24 cm.
- 5.24 — leg² = 25² − 7² = 625 − 49 = 576, so the leg = 24 cm.
- 6.12 — leg² = 15² − 9² = 225 − 81 = 144, so the leg = 12 cm.
- 7.52 — length² = 20² + 48² = 2704, so the sloped surface is 52 cm.
- 8.10 — length² = 6² + 8² = 100, so the sloped surface is 10 cm.
- 9.34 — length² = 16² + 30² = 1156, so the sloped surface is 34 cm.