Asked by bruh no
If the hypotenuse of a triangle is 13, and one side length is 5, what is the second side length?
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12
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7
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12
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Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find the length of the second side of the right triangle, we can use the Pythagorean theorem, which states:
\[
a^2 + b^2 = c^2
\]
where \(c\) is the length of the hypotenuse and \(a\) and \(b\) are the lengths of the other two sides. Here, we know:
- \(c = 13\)
- \(a = 5\)
- \(b = ?\)
Plugging the known values into the equation:
\[
5^2 + b^2 = 13^2
\]
Calculating \(5^2\) and \(13^2\):
\[
25 + b^2 = 169
\]
Now, isolate \(b^2\) by subtracting 25 from both sides:
\[
b^2 = 169 - 25
\]
\[
b^2 = 144
\]
Taking the square root of both sides gives us:
\[
b = \sqrt{144} = 12
\]
Therefore, the length of the second side is **12**.
\[
a^2 + b^2 = c^2
\]
where \(c\) is the length of the hypotenuse and \(a\) and \(b\) are the lengths of the other two sides. Here, we know:
- \(c = 13\)
- \(a = 5\)
- \(b = ?\)
Plugging the known values into the equation:
\[
5^2 + b^2 = 13^2
\]
Calculating \(5^2\) and \(13^2\):
\[
25 + b^2 = 169
\]
Now, isolate \(b^2\) by subtracting 25 from both sides:
\[
b^2 = 169 - 25
\]
\[
b^2 = 144
\]
Taking the square root of both sides gives us:
\[
b = \sqrt{144} = 12
\]
Therefore, the length of the second side is **12**.
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