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Rectangle and Point










































ABCD is a rectangle and P is a point inside the rectangle. If PA = 3, PB = 4, PC = 5 ,
find the exact value of PD, in simplified form.

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Nov 22, 2011
Rectangle and Interior Point
by: Staff



Question:


ABCD is a rectangle and P is a point inside the rectangle. If PA = 3, PB = 4, PC = 5 ,
find the exact value of PD, in simplified form.

Answer:


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For any point P within a rectangle ABCD:


(PA)² + (PC)² = (PB)² + (PD)²

3² + 5² = 4² + (PD)²

9 + 25 = 16 + (PD)²

34 = 16 + (PD)²

34 - 16 = 16 - 16 + (PD)²

18 = 0 + (PD)²

18 = (PD)²

(PD)² = 18

√[(PD)²] = √(18)

PD = √(2*3²)

PD = 3√(2)


The final answer to your question is: PD = 3√(2)




Thanks for writing.

Staff
www.solving-math-problems.com



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