Let's analyze Jeremy's explanation step-by-step to identify any inaccuracies.
Step 1:
[tex]\[ 35^2 + 30^2 ? 60^2 \][/tex]
Jeremy is setting up the equation to check if it holds true for a right-angled triangle using the Pythagorean theorem. This is correct as a starting point. The Pythagorean theorem states that for a right triangle with legs [tex]\(a\)[/tex], [tex]\(b\)[/tex], and hypotenuse [tex]\(c\)[/tex]:
[tex]\[ a^2 + b^2 = c^2 \][/tex]
Step 2:
[tex]\[ (35 + 30)^2 = 60^2 \][/tex]
Jeremy combined the terms incorrectly here. The correct approach should have been to calculate [tex]\(35^2\)[/tex] and [tex]\(30^2\)[/tex] individually and then check their sum against [tex]\(60^2\)[/tex]:
- [tex]\(35^2 = 1225\)[/tex]
- [tex]\(30^2 = 900\)[/tex]
Adding these:
[tex]\[ 1225 + 900 = 2125 \][/tex]
So, comparing 2125 to [tex]\(60^2\)[/tex] gives us:
[tex]\[ 2125 \neq 3600 \][/tex]
Jeremy's error was in combining the terms under one square, which is not a property of the Pythagorean theorem.
Step 3:
[tex]\[ 65^2 = 60^2 \][/tex]
When Jeremy combined the terms as [tex]\( (35 + 30)^2 = 65^2 \)[/tex], he made a fundamental mistake. In the context of the Pythagorean theorem, we are not allowed to add the lengths of the legs before squaring them. Instead, each leg must be squared individually and sum them up.
Step 4:
[tex]\[ 4225 \neq 3600 \][/tex]
The numbers Jeremy calculated in Step 3 are irrelevant as the approach was wrong in Step 2.
Conclusion:
Jeremy's explanation contains inaccuracies, primarily in Step 2 where he incorrectly combined the terms. He should have calculated [tex]\(35^2\)[/tex] and [tex]\(30^2\)[/tex] separately and compared their sum to [tex]\(60^2\)[/tex].
From the choices given:
- Jeremy's explanation is inaccurate. He incorrectly combined terms in step 2.
This description best suits the analysis of Jeremy's explanation.
