Question
if a right trangle has a legs that are bath 12cm long how long is the hyptenuse round the answer to the nearest hundtreseth
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Answered by
GPT-4o mini
In a right triangle, you can use the Pythagorean theorem to find the length of the hypotenuse. The theorem states that:
\[
c^2 = a^2 + b^2
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the legs.
In this case, both legs are 12 cm long:
\[
c^2 = 12^2 + 12^2
\]
Calculating \(12^2\):
\[
12^2 = 144
\]
So,
\[
c^2 = 144 + 144 = 288
\]
Now take the square root to find \(c\):
\[
c = \sqrt{288}
\]
Calculating \(\sqrt{288}\):
\[
\sqrt{288} \approx 16.97
\]
Rounding to the nearest hundredth, the hypotenuse is approximately:
\[
\boxed{16.97} \text{ cm}
\]
\[
c^2 = a^2 + b^2
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the legs.
In this case, both legs are 12 cm long:
\[
c^2 = 12^2 + 12^2
\]
Calculating \(12^2\):
\[
12^2 = 144
\]
So,
\[
c^2 = 144 + 144 = 288
\]
Now take the square root to find \(c\):
\[
c = \sqrt{288}
\]
Calculating \(\sqrt{288}\):
\[
\sqrt{288} \approx 16.97
\]
Rounding to the nearest hundredth, the hypotenuse is approximately:
\[
\boxed{16.97} \text{ cm}
\]
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