Question

on a recent test, shawna was given the following problem.

1. ( a^{2}+7^{2}=25^{2} )
2. ( a^{2}+14 = 50 )
3. ( a^{2}=36 )
4. ( a = 6 mathrm{~m} )

in which step did shawna make an error?
step 1. she incorrectly applied the pythagorean theorem.
step 2. she incorrectly squared the numbers.
step 3. she incorrectly isolated ( a^{2} ).
step 4. she incorrectly solved for ( a ).

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here \(b = 7\), \(c = 25\), so \(a^{2}+7^{2}=25^{2}\) is correct (Step 1 is correct).

Step2: Square the numbers

\(7^{2}=49\), \(25^{2}=625\). The equation should be \(a^{2}+49 = 625\), but Shawna wrote \(a^{2}+14 = 50\) (incorrect squaring in Step 2).

Step3: Isolate \(a^{2}\)

If the correct equation \(a^{2}+49 = 625\) is used, then \(a^{2}=625 - 49=576\). But with Shawna's wrong equation \(a^{2}+14 = 50\), \(a^{2}=50 - 14 = 36\) (error in Step 2 leads to wrong isolation in Step 3).

Step4: Solve for \(a\)

If \(a^{2}=576\), then \(a = 24\). If \(a^{2}=36\), then \(a = 6\) (error in Step 2 leads to wrong solution in Step 4).

Answer:

Step 2. She incorrectly squared the numbers.