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A triangle has sides with lengths of 14miles14\,\text{miles}, 15miles15\,\text{miles}, and 18miles18\,\text{miles}. Is it a right triangle?\newlineChoices:\newline(A)yes\newline(B)no

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Q. A triangle has sides with lengths of 14miles14\,\text{miles}, 15miles15\,\text{miles}, and 18miles18\,\text{miles}. Is it a right triangle?\newlineChoices:\newline(A)yes\newline(B)no
  1. Identify longest side: Step 11: Identify the longest side to test for the hypotenuse.\newlineGiven side lengths: 1414 miles, 1515 miles, 1818 miles.\newlineThe longest side, which could be the hypotenuse, is 1818 miles.
  2. Apply Pythagorean Theorem: Step 22: Apply the Pythagorean Theorem to check if it's a right triangle.\newlineUsing the formula a2+b2=c2a^2 + b^2 = c^2, where cc is the hypotenuse.\newlineCalculate 142+15214^2 + 15^2 and compare it to 18218^2.\newline142=19614^2 = 196, 152=22515^2 = 225, 182=32418^2 = 324.\newline196+225=421196 + 225 = 421.
  3. Compare sum of squares: Step 33: Compare the sum of squares of the shorter sides to the square of the longest side.\newline421421 does not equal 324324.\newlineSince 421324421 \neq 324, the triangle is not a right triangle.

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