Question

How do I find the length of the hypotenuse in a right triangle with legs of equal length, where both legs are 12 cm long, and round the answer to the nearest hundredth?

Answer 1

To find the length of the hypotenuse in a right triangle with legs of equal length, you can use the Pythagorean theorem, which states:

\[
c^2 = a^2 + b^2
\]

In your case, both legs \( a \) and \( b \) are equal to 12 cm:

\[
c^2 = 12^2 + 12^2
\]

Calculating \( 12^2 \):

\[
12^2 = 144
\]

Now plug this value into the equation:

\[
c^2 = 144 + 144
\]
\[
c^2 = 288
\]

Next, solve for \( c \) by taking the square root of both sides:

\[
c = \sqrt{288}
\]

To find \( \sqrt{288} \), you can simplify it as follows:

\[
\sqrt{288} = \sqrt{144 \times 2} = \sqrt{144} \times \sqrt{2} = 12 \sqrt{2}
\]

Calculating \( \sqrt{2} \) (approximately 1.414):

\[
c \approx 12 \times 1.414 \approx 16.968
\]

Now, rounding to the nearest hundredth:

\[
c \approx 16.97 \text{ cm}
\]

Therefore, the length of the hypotenuse is approximately \( \boxed{16.97} \) cm.