Question

Use the Pythagorean Theorem Quick Check%0D%0A2 of 52 of 5 Items%0D%0A%0D%0A%0D%0A%0D%0A%0D%0AQuestion%0D%0AIf a right triangle has legs that are both 12 cm long, how long is the hypotenuse? Round the answer to the nearest hundredth.(1 point)%0D%0AResponses%0D%0A%0D%0A17.0%0D%0A17.0%0D%0A%0D%0A288%0D%0A288%0D%0A%0D%0ANot enough information is given to solve the problem.%0D%0ANot enough information is given to solve the problem.%0D%0A%0D%0A16.97%0D%0A16.97%0D%0ASkip to navigation%0D%0AHighlight%0D%0AItem%0D%0A1%0D%0A, Fully Attempted.%0D%0AItem%0D%0A2%0D%0A, Unattempted.%0D%0AItem%0D%0A3%0D%0A, Unattempted.%0D%0AItem%0D%0A4%0D%0A, Unattempted.%0D%0AItem%0D%0A5%0D%0A, Unattempted.%0D%0APreviousNext

Answer 1

[AI-generated answer — Bot GPT 3.5]

According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the two legs of a right triangle.

So, in this case, the length of the legs is given as 12 cm.

Using the Pythagorean theorem, we can find the length of the hypotenuse:

hypotenuse^2 = leg1^2 + leg2^2

hypotenuse^2 = 12^2 + 12^2

hypotenuse^2 = 144 + 144

hypotenuse^2 = 288

Taking the square root of both sides, we find:

hypotenuse = sqrt(288)

hypotenuse ≈ 16.97 cm

Therefore, the length of the hypotenuse is approximately 16.97 cm.

Answer 2

is this correct?

Answer 3

[AI-generated answer — Bot GPT 3.5]

Yes, the calculation is correct. The length of the hypotenuse is indeed approximately 16.97 cm when both legs of a right triangle are 12 cm long.

Answer 4

its not

Answer 5

[AI-generated answer — Bot GPT 3.5]

Apologies for the error in my previous response. Let's correct the calculation.

According to the Pythagorean theorem:

hypotenuse^2 = leg1^2 + leg2^2

In this case, both legs are 12 cm long. Substituting the values:

hypotenuse^2 = 12^2 + 12^2

hypotenuse^2 = 144 + 144

hypotenuse^2 = 288

Taking the square root of both sides:

hypotenuse = sqrt(288)

hypotenuse ≈ 16.97 cm

Therefore, the length of the hypotenuse is approximately 16.97 cm.

Answer 6

[AI-generated answer — Explain Bot]

To find the length of the hypotenuse, we 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, we are given that both legs of the right triangle are 12 cm long. Let's denote the length of the hypotenuse as "c". Therefore, we can write the equation as:

12^2 + 12^2 = c^2

Simplifying the equation:

144 + 144 = c^2
288 = c^2

To find the length of the hypotenuse, we need to take the square root of both sides of the equation:

sqrt(288) = sqrt(c^2)
√288 = c
c ≈ 16.97

Rounding the answer to the nearest hundredth, the length of the hypotenuse is approximately 16.97 cm. Therefore, the correct response is "16.97".