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Question
Mathematics
In the figure below, P R = 32 PR=32 and Q R = 14 QR=14. Find P Q PQ.
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From the given information, we can use the Pythagorean theorem to find P R PR and Q R QR:
P R 2 = P Q 2 + Q R 2 PR^(2)=PQ^(2)+QR^(2)
32 2 = P Q 2 + 14 2 32^(2)=PQ^(2)+14^(2)
Simplifying this equation, we get:
1024 = P Q 2 + 196 1024=PQ^(2)+196
Subtracting 196 from both sides, we get:
828 = P Q 2 828=PQ^(2)
Taking the square root of both sides, we get:
P Q = 828 28.77 PQ=sqrt828~~28.77
Therefore, P Q 28.77 PQ~~28.77.
Step-by-step solution:
  1. Use the Pythagorean theorem to find P R PR: P R 2 = P Q 2 + Q R 2 PR^(2)=PQ^(2)+QR^(2)
  2. Substitute the given values for P R PR and Q R QR: 32 2 = P Q 2 + 14 2 32^(2)=PQ^(2)+14^(2)
  3. Simplify the equation: 1024 = P Q 2 + 196 1024=PQ^(2)+196
  4. Solve for P Q PQ: P Q 2 = 828 PQ^(2)=828
  5. Take the square root of both sides: P Q = 828 28.77 PQ=sqrt828~~28.77
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