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Problem 401

A triangle has sides that measure 20,21 , and 29 inches. Determine whether the triangle is a right triangle.

Short Answer

Expert verified
The triangle with sides measuring 20 inches, 21 inches, and 29 inches does not satisfy the Pythagorean theorem (a^2 + b^2 = c^2) for any combination of sides, so it is not a right triangle.
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Step by step solution

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Step 1: Identify and label the sides

Let's label the given side lengths as a, b, and c, where: a = 20 inches b = 21 inches c = 29 inches

Step 2: Test the Pythagorean theorem for each combination of sides

We will test the Pythagorean theorem (a^2 + b^2 = c^2) for each combination of sides, and check if any of the combinations satisfy the equation: 1. Assuming a = 20 inches and b = 21 inches are the legs and c = 29 inches is the hypotenuse: \(20^2 + 21^2 = 29^2\) \(400 + 441 \neq 841\) \(841 \neq 841\) 2. Assuming a = 20 inches and c = 29 inches are the legs and b = 21 inches is the hypotenuse: \(20^2 + 29^2 = 21^2\) \(400 + 841 \neq 441\) \(1241 \neq 441\) 3. Assuming b = 21 inches and c = 29 inches are the legs and a = 20 inches is the hypotenuse: \(21^2 + 29^2 = 20^2\) \(441 + 841 \neq 400\) \(1282 \neq 400\)

Step 3: Conclusion

Since none of the combinations of sides satisfy the Pythagorean theorem (a^2 + b^2 = c^2), we can conclude that the triangle with sides measuring 20 inches, 21 inches, and 29 inches is not a right triangle.

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