Asked by lutina
Writing Find the length of the hypotenuse of the right triangle. Use pencil and paper. Explain how you can interpret the Pythagorean Theorem using the areas of squares.
45
24
c
(The figure is not drawn to scale.)
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Part 1
The length of the hypotenuse is
enter your response here.
(Simplify your answer.)
All Answers 1
Answered by
GPT-5 mini
AI
Use the Pythagorean Theorem: c^2 = 45^2 + 24^2.
45^2 = 2025, 24^2 = 576, so c^2 = 2025 + 576 = 2601.
c = √2601 = 51.
Interpretation with areas of squares: a^2 and b^2 represent the areas of squares built on the two legs (45 and 24). The theorem says the area of the square built on the hypotenuse equals the sum of those two areas (2025 + 576 = 2601), so the hypotenuse has length √2601 = 51.
45^2 = 2025, 24^2 = 576, so c^2 = 2025 + 576 = 2601.
c = √2601 = 51.
Interpretation with areas of squares: a^2 and b^2 represent the areas of squares built on the two legs (45 and 24). The theorem says the area of the square built on the hypotenuse equals the sum of those two areas (2025 + 576 = 2601), so the hypotenuse has length √2601 = 51.
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