Problem Solving with Pythagorean Triples

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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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| Attempts: 13 | Questions: 10 | Updated: Dec 9, 2025
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Question 1 / 11
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1) If x² + y² = z², and x = 15, y = 20, what is z?

Explanation

√(225+400)=√625=25.

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About This Quiz
Problem Solving With Pythagorean Triples - Quiz

Can you use Pythagorean triples to solve real problems? In this quiz, you’ll apply triples to ladders, ramps, triangle perimeters, and areas. We bring you this quiz so you can see how these sets of numbers aren’t just theory—they’re powerful tools for solving geometry problems quickly.

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2) A right triangle has legs of 9 and 40. The hypotenuse is:

Explanation

√(81+1600)=√1681=41.

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3) If (a, b, c) = (21, 28, 35), this triple is:

Explanation

Divide by 7 → (3,4,5).

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4) A triangle has sides (11, 60, 61). Its hypotenuse is:

Explanation

11²+60²=3721=61².

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5) A ladder leans against a wall, 15 ft high, with its base 8 ft away. How long is the ladder?

Explanation

√(15²+8²)=√(289)=17 ft.

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6) A right triangle has hypotenuse 25 and one leg 7. The other leg is:

Explanation

√(25²–7²)=√(576)=24.

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7) The perimeter of a (5, 12, 13) triangle is:

Explanation

5+12+13=30.

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8) If the area of a right triangle is 24, with legs in a (3, 4, 5) ratio, what are the legs?

Explanation

Area=½ab=24 → ab=48 → scale factor 2.

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9) A square is built on each side of a (5, 12, 13) triangle. The sum of the areas of the two smaller squares is:

Explanation

Follows a²+b²=c².

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10) Which triple can represent the side lengths of a triangle?

Explanation

Each satisfies a²+b²=c².

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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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If x² + y² = z², and x = 15, y = 20, what is z?
A right triangle has legs of 9 and 40. The hypotenuse is:
If (a, b, c) = (21, 28, 35), this triple is:
A triangle has sides (11, 60, 61). Its hypotenuse is:
A ladder leans against a wall, 15 ft high, with its base 8 ft away....
A right triangle has hypotenuse 25 and one leg 7. The other leg is:
The perimeter of a (5, 12, 13) triangle is:
If the area of a right triangle is 24, with legs in a (3, 4, 5) ratio,...
A square is built on each side of a (5, 12, 13) triangle. The sum of...
Which triple can represent the side lengths of a triangle?
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