To determine if Jerrod's calculation is correct, let’s analyze the steps he took using the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, \( c^2 = a^2 + b^2 \), where \( c \) is the hypotenuse, and \( a \) and \( b \) are the lengths of the legs.
In this case:
- One leg (a) is 3 ft.
- The other leg (b) is 1 ft.
Calculating the hypotenuse:
\[ c^2 = a^2 + b^2 \] \[ c^2 = 3^2 + 1^2 \] \[ c^2 = 9 + 1 \] \[ c^2 = 10 \]
Now, taking the square root to find \( c \):
\[ c = \sqrt{10} \]
Now let’s review Jerrod's work:
- He wrote that \( c^2 = 3^2 + 1^2 \) as \( c^2 = 32 + 12 \), which is incorrect. It should have been \( c^2 = 9 + 1 \). This shows that he misrepresented the squares of the legs.
- Correctly, it continues with \( c^2 = 10 \), but he ended with \( c^2 = 8 \).
So, to answer the question:
No, he set up the Pythagorean theorem incorrectly.
This is because he incorrectly calculated the squares and ended with an incorrect sum.
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