In a right-angled triangle, the lengths of the two legs are 9 and 12. Find the length of the hypoten

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In a right-angled triangle, the lengths of the two legs are 9 and 12. Find the length of the hypotenuse.

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{"content":[{"content":[{"text":"Step 1:","type":"text","marks":[{"type":"bold"}]},{"text":" Let the legs of the right triangle be ","type":"text"},{"attrs":{"latex":"a = 9"},"type":"math_inline"},{"text":" and ","type":"text"},{"attrs":{"latex":"b = 12"},"type":"math_inline"},{"text":", and the hypotenuse be ","type":"text"},{"attrs":{"latex":"c"},"type":"math_inline"},{"text":". By the Pythagorean Theorem:","type":"text"}],"type":"paragraph"},{"type":"math_block","attrs":{"latex":"c^2 = a^2 + b^2"}},{"content":[{"text":"Step 2:","type":"text","marks":[{"type":"bold"}]},{"text":" Substitute the values:","type":"text"}],"type":"paragraph"},{"type":"math_block","attrs":{"latex":"c^2 = 9^2 + 12^2 = 81 + 144 = 225"}},{"content":[{"marks":[{"type":"bold"}],"text":"Step 3:","type":"text"},{"text":" Take the square root of both sides:","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"c = \sqrt{225} = 15"},"type":"math_block"},{"type":"paragraph","content":[{"text":"So the length of the hypotenuse is ","type":"text"},{"attrs":{"latex":"15"},"type":"math_inline"},{"text":". Note that this is a scaled version of the famous ","type":"text"},{"attrs":{"latex":"3-4-5"},"type":"math_inline"},{"text":" Pythagorean triple (scaled by factor of 3).","type":"text"}]}],"type":"doc"}

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