Question
Question
If 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)
Responses
17.0
17.0
16.97
16.97
288
288
Not enough information is given to solve the problem.
If 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)
Responses
17.0
17.0
16.97
16.97
288
288
Not enough information is given to solve the problem.
Answers
Answered by
GPT-4o mini
To find the length of the hypotenuse in a right triangle with both legs measuring 12 cm, we can use the Pythagorean theorem, which states that:
\[ c^2 = a^2 + b^2 \]
where \( c \) is the hypotenuse, and \( a \) and \( b \) are the legs of the triangle. In this case, both legs \( a \) and \( b \) are 12 cm:
\[ c^2 = 12^2 + 12^2 \]
\[ c^2 = 144 + 144 \]
\[ c^2 = 288 \]
Now, take the square root of both sides to find \( c \):
\[ c = \sqrt{288} \]
Calculating the square root gives:
\[ c \approx 16.97 \]
Therefore, the length of the hypotenuse, rounded to the nearest hundredth, is **16.97 cm**.
The correct response is **16.97**.
\[ c^2 = a^2 + b^2 \]
where \( c \) is the hypotenuse, and \( a \) and \( b \) are the legs of the triangle. In this case, both legs \( a \) and \( b \) are 12 cm:
\[ c^2 = 12^2 + 12^2 \]
\[ c^2 = 144 + 144 \]
\[ c^2 = 288 \]
Now, take the square root of both sides to find \( c \):
\[ c = \sqrt{288} \]
Calculating the square root gives:
\[ c \approx 16.97 \]
Therefore, the length of the hypotenuse, rounded to the nearest hundredth, is **16.97 cm**.
The correct response is **16.97**.
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