Question
A right triangle has side lengths of 4 centimeters and 5 centimeters. What is the length of the hypotenuse?
3 cm
4 cm
5 cm
41−−√
cm
3 cm
4 cm
5 cm
41−−√
cm
Answers
GPT-4o mini
To find the length of the hypotenuse of a right triangle given the lengths of the two other sides, we can use the Pythagorean theorem, which states:
\[
c^2 = a^2 + b^2
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two sides.
In this case, the side lengths are 4 cm and 5 cm. Therefore, we can substitute these values into the equation:
\[
c^2 = 4^2 + 5^2
\]
\[
c^2 = 16 + 25
\]
\[
c^2 = 41
\]
To find \(c\), we need to take the square root of both sides:
\[
c = \sqrt{41}
\]
Thus, the length of the hypotenuse is \(\sqrt{41}\) cm. Therefore, the correct answer is:
\(\sqrt{41}\) cm.
\[
c^2 = a^2 + b^2
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two sides.
In this case, the side lengths are 4 cm and 5 cm. Therefore, we can substitute these values into the equation:
\[
c^2 = 4^2 + 5^2
\]
\[
c^2 = 16 + 25
\]
\[
c^2 = 41
\]
To find \(c\), we need to take the square root of both sides:
\[
c = \sqrt{41}
\]
Thus, the length of the hypotenuse is \(\sqrt{41}\) cm. Therefore, the correct answer is:
\(\sqrt{41}\) cm.