If a right triangle has legs that are both 12 cm long, how long is the hypotenuse? Round the answer to the nearest hundredth.
To find the length of the hypotenuse in a right triangle, we can use the Pythagorean theorem: $a^2 + b^2 = c^2$, where $a$ and $b$ are the lengths of the legs, and $c$ is the length of the hypotenuse.
In this case, both legs are 12 cm long. Substituting these lengths into the equation, we have $12^2 + 12^2 = c^2$.
Simplifying the equation, we find $144 + 144 = c^2$.
Adding the numbers on the left side, we get $288 = c^2$.
To solve for $c$, we can take the square root of both sides: $\sqrt{288} = \sqrt{c^2}$.
Since we're asked to round the answer to the nearest hundredth, we have $c \approx \sqrt{288} \approx 16.97$.
Therefore, the length of the hypotenuse is approximately 16.97 cm.
To find the length of the hypotenuse of a right triangle, you can use the Pythagorean Theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the legs (a and b).
In this case, both legs are 12 cm long, so a = b = 12 cm.
Using the Pythagorean Theorem, we can solve for c:
c^2 = a^2 + b^2
c^2 = 12^2 + 12^2
c^2 = 144 + 144
c^2 = 288
To find the length of c, we take the square root of both sides:
c = sqrt(288)
c ≈ 16.97 cm
Therefore, the approximate length of the hypotenuse is 16.97 cm (rounded to the nearest hundredth).
To find the length of the hypotenuse in a right triangle, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.
In this case, both legs are 12 cm. So, let's call one leg "a" and the other leg "b." Applying the Pythagorean theorem, we have:
a^2 + b^2 = c^2
Substituting the values, we get:
12^2 + 12^2 = c^2
Simplifying:
144 + 144 = c^2
288 = c^2
To find c, we need to take the square root of both sides:
sqrt(288) = sqrt(c^2)
c ≈ 16.97 cm (rounded to the nearest hundredth)
Therefore, using the Pythagorean theorem, the length of the hypotenuse in this right triangle is approximately 16.97 cm.