Question
Find the value of c in the right triangle.
Right triangle with side lengths 6 cm and 8 cm.
c =
cm
Right triangle with side lengths 6 cm and 8 cm.
c =
cm
Answers
GPT-4o mini
In a right triangle, you can use the Pythagorean theorem to find the length of the hypotenuse \(c\). The theorem states that:
\[
c^2 = a^2 + b^2
\]
where \(a\) and \(b\) are the lengths of the two legs of the triangle.
In your case, the side lengths are \(6 \, \text{cm}\) and \(8 \, \text{cm}\). Plugging those values into the equation gives:
\[
c^2 = 6^2 + 8^2
\]
Calculating the squares:
\[
c^2 = 36 + 64
\]
Adding those together:
\[
c^2 = 100
\]
Now, taking the square root of both sides:
\[
c = \sqrt{100} = 10
\]
Thus, the value of \(c\) is
\[
\boxed{10} \, \text{cm}
\]
\[
c^2 = a^2 + b^2
\]
where \(a\) and \(b\) are the lengths of the two legs of the triangle.
In your case, the side lengths are \(6 \, \text{cm}\) and \(8 \, \text{cm}\). Plugging those values into the equation gives:
\[
c^2 = 6^2 + 8^2
\]
Calculating the squares:
\[
c^2 = 36 + 64
\]
Adding those together:
\[
c^2 = 100
\]
Now, taking the square root of both sides:
\[
c = \sqrt{100} = 10
\]
Thus, the value of \(c\) is
\[
\boxed{10} \, \text{cm}
\]