If a right triangle has legs that are both 12cm long, how long is the hypotenuse? Round the answer to the nearest hundredth.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
a^2 + b^2 = c^2
where a and b are the lengths of the legs, and c is the length of the hypotenuse.
Substituting the values we know:
12^2 + 12^2 = c^2
144 + 144 = c^2
288 = c^2
Taking the square root of both sides:
c = √288
c ≈ 16.97
Therefore, the length of the hypotenuse is approximately 16.97 cm.
To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs.
Let's call the length of the hypotenuse "c" and the length of each leg "a" (both equal to 12cm).
According to the Pythagorean theorem:
c^2 = a^2 + a^2
Simplifying this equation, we have:
c^2 = 2a^2
To solve for the length of the hypotenuse, we can take the square root of both sides:
c = √(2a^2)
Substituting the value of "a" as 12cm:
c = √(2(12cm)^2)
Now let's calculate the length of the hypotenuse:
c = √(2(144cm^2))
c = √(288cm^2)
c ≈ 16.97 cm
Therefore, the length of the hypotenuse is approximately 16.97 cm when both legs of the right triangle are 12 cm long (rounded to the nearest hundredth).
To find the length of the hypotenuse in a right triangle, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. In mathematical terms:
a^2 + b^2 = c^2
Here, "a" and "b" represent the lengths of the legs, and "c" represents the length of the hypotenuse. In this case, both legs are 12 cm long. So, we can plug these values into the theorem:
12^2 + 12^2 = c^2
Simplifying the equation:
144 + 144 = c^2
288 = c^2
To find the value of "c," we need to take the square root of both sides of the equation:
√288 = √c^2
c ≈ 16.97
Therefore, the length of the hypotenuse, rounded to the nearest hundredth, is approximately 16.97 cm.