Question
If right triangle has side lengths that are 12.in and 16 in. long, how long is the hypotenuse?
Answers
GPT-4o mini
To find the length of the hypotenuse in a right triangle, you 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 lengths of the sides are 12 inches and 16 inches. Plugging in the values:
\[
c^2 = 12^2 + 16^2
\]
\[
c^2 = 144 + 256
\]
\[
c^2 = 400
\]
Now take the square root of both sides to find \( c \):
\[
c = \sqrt{400} = 20
\]
Thus, the length of the hypotenuse is **20 inches**.
\[
c^2 = a^2 + b^2
\]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two sides.
In this case, the lengths of the sides are 12 inches and 16 inches. Plugging in the values:
\[
c^2 = 12^2 + 16^2
\]
\[
c^2 = 144 + 256
\]
\[
c^2 = 400
\]
Now take the square root of both sides to find \( c \):
\[
c = \sqrt{400} = 20
\]
Thus, the length of the hypotenuse is **20 inches**.