What is the length of the hypotenuse, rounded to the nearest tenth, of a right triangle with sides of length 60m and 80m?
Understand the Problem
The question asks to find the length of the hypotenuse of a right triangle given the lengths of the other two sides, 60m and 80m. We can solve this using the Pythagorean theorem ($a^2 + b^2 = c^2$), where 'a' and 'b' are the lengths of the two sides, and 'c' is the length of the hypotenuse. The final answer should be rounded to the nearest tenth.
Answer
$100.0$ m
Answer for screen readers
$100.0$ m
Steps to Solve
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Apply the Pythagorean theorem Use the Pythagorean theorem $a^2 + b^2 = c^2$, where $a = 60$ m and $b = 80$ m.
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Substitute the values of $a$ and $b$ Substitute the given values of $a$ and $b$ into the equation: $60^2 + 80^2 = c^2$
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Calculate the squares Calculate the squares of 60 and 80: $3600 + 6400 = c^2$
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Add the squared values Add the two values: $10000 = c^2$
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Find the square root Take the square root of both sides of the equation to solve for $c$: $c = \sqrt{10000}$
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Calculate the square root Calculate the square root of 10000: $c = 100$
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Write the final answer with units Since the sides are given in meters, the hypotenuse is also in meters: $c = 100$ m
$100.0$ m
More Information
The triangle with sides 60, 80, and 100 is a multiple of the 3-4-5 right triangle (multiplied by 20).
Tips
A common mistake is forgetting to take the square root after summing the squares of the two sides. Another mistake might be mixing up which side is the hypotenuse and which are the legs of the triangle.
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