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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.

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.
See the step by step solution

## 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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