Math Problem Statement
Solution
The worksheet contains problems involving the Pythagorean Theorem and Pythagorean Triples. Let's solve each question in sequence.
Example 1: Using the Pythagorean Theorem
The Pythagorean Theorem states:
where is the hypotenuse of a right triangle, and and are the other two sides.
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Problem 1: Both legs are 3.
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Problem 2: Legs are 9 and 12; hypotenuse is .
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Problem 3: One leg is 25, hypotenuse is 65, find the other leg .
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Problem 4: Legs are 5 and 9; hypotenuse is .
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Problem 5: Legs are 16 and 33; hypotenuse is .
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Problem 6: Legs are 11 and 28; hypotenuse is .
Example 2: Using Pythagorean Triples
In this section, the problems involve recognizing patterns of Pythagorean triples, which are sets of three integers that satisfy the Pythagorean Theorem.
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Problem 7: Known triple ; so .
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Problem 8: Known triple , scaled by 5 to , so .
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Problem 9: Known triple , scaled by 4 to , so .
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Problem 10: Known triple ; so .
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Problem 11: Known triple ; so .
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Problem 12: Known triple , scaled by 4 to , so .
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Math Problem Analysis
Mathematical Concepts
Geometry
Right Triangles
Pythagorean Theorem
Pythagorean Triples
Formulas
a^2 + b^2 = c^2
Theorems
Pythagorean Theorem
Suitable Grade Level
Grades 8-10
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