On a recent test, Shawna was given the following problem:

Question

Shawna's work is shown below:

Step 1: a2+72=252

Step 2: a2+14=50

Step 3: a2=36

a=6 m

In which step did Shawna make an error?

(1 point)
Responses

Step 3. She incorrectly isolated a2
Step 3. She incorrectly isolated A squared

Step 1. She incorrectly applied the Pythagorean theorem.
Step 1. She incorrectly applied the Pythagorean theorem.

Step 2. She incorrectly squared the numbers.
Step 2. She incorrectly squared the numbers.

Step 4. She incorrectly solved for a

Answer 1

To identify where Shawna made an error, let's analyze the steps she presented:

1. Step 1: a² + 72 = 252

   • This seems to set up an equation, possibly related to a right triangle using the Pythagorean theorem. However, we first need to examine if this setup is correct based on the context provided.

2. Step 2: a² + 14 = 50

   • This appears to be a manipulation of Step 1. If we subtract 72 from both sides of Step 1, we should have: \[ a² = 252 - 72 \] Calculating that gives: \[ a² = 180 \] which is different from what is in Step 2. Therefore, Step 2 is incorrect.

3. Step 3: a² = 36

   • If Step 2 were correct, it should lead us to a different value for \( a² \). Thus, Step 3 is also incorrect.

4. Final Step: a = 6 m

   • This follows from Step 3. Since Step 3 is inaccurate, this conclusion also is incorrect.

Based on the above analysis, the error occurs in Step 2, where she incorrectly manipulated or squared the numbers.

So the correct response is: Step 2. She incorrectly squared the numbers.