Find $P B$ , given that $P A = 15, P C = 20, P D = 7$ , and $A B C D$ is a square.

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Solution

$\begin{matrix} (1) P A^{2} = x^{2} + {(h - y)}^{2} = 15^{2} (2) P C^{2} = (h - x) + y^{2} = 400 (3) P D^{2} = x^{2} + y^{2} = 49 ∴ x^{2} + {(h - y)}^{2} + {(h - x)}^{2} + y^{2} - x^{2} - y^{2} = 225 + 400 - 49 {(h - y)}^{2} + {(h - x)}^{2} = 576 P B^{2} = 576 P B = 24 \end{matrix}$

Hence, this is the answer.

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Find PB, given that PA=15,PC=20,PD=7, and ABCD is a square.

(1)PA2=x2+(h−y)2=152(2)PC2=(h−x)+y2=400(3)PD2=x2+y2=49∴x2+(h−y)2+(h−x)2+y2−x2−y2=225+400−49(h−y)2+(h−x)2=576PB2=576PB=24Hence, this is the answer.

Find $P B$ , given that $P A = 15, P C = 20, P D = 7$ , and $A B C D$ is a square.