Praxis 5003 Practice Test Practice Question
In the equation a^2+b^2=c^2, a=24 and c=25. If b>0, what is the value of b?
Correct Answer: b=7
Rationale: To find the value of \( b \) in the equation \( a^2 + b^2 = c^2 \), substitute \( a = 24 \) and \( c = 25 \). Calculating \( 24^2 + b^2 = 25^2 \) gives \( 576 + b^2 = 625 \). Solving for \( b^2 \) results in \( b^2 = 625 - 576 = 49 \), leading to \( b = 7 \) since \( b \) must be positive.
Other options are incorrect because:
- If \( b = 24 \), the equation does not hold, as \( 24^2 + 24^2 \neq 25^2 \).
- If \( b = 8 \), substituting yields \( 576 + 64 \neq 625 \).
- If \( b = 6 \), substituting gives \( 576 + 36 \neq 625 \).
Thus, the only value that satisfies the equation is \( b = 7 \).
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