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
288
288
17.0
17.0
16.97
16.97
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
288
288
17.0
17.0
16.97
16.97
Not enough information is given to solve the problem.
Answers
GPT-4o mini
To find the length of the hypotenuse of a right triangle with legs of equal length (both 12 cm), you can use the Pythagorean theorem, which states:
\[ c^2 = a^2 + b^2 \]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the legs.
In this case:
- \( a = 12 \) cm
- \( b = 12 \) cm
So we have:
\[ c^2 = 12^2 + 12^2 \]
\[ c^2 = 144 + 144 \]
\[ c^2 = 288 \]
Now, take the square root of both sides to find \( c \):
\[ c = \sqrt{288} \]
Calculating that gives:
\[ c \approx 16.97 \] cm (to two decimal places)
So the hypotenuse is approximately **16.97 cm**.
The correct response is:
**16.97**
\[ c^2 = a^2 + b^2 \]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the legs.
In this case:
- \( a = 12 \) cm
- \( b = 12 \) cm
So we have:
\[ c^2 = 12^2 + 12^2 \]
\[ c^2 = 144 + 144 \]
\[ c^2 = 288 \]
Now, take the square root of both sides to find \( c \):
\[ c = \sqrt{288} \]
Calculating that gives:
\[ c \approx 16.97 \] cm (to two decimal places)
So the hypotenuse is approximately **16.97 cm**.
The correct response is:
**16.97**