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Find length BC.

 

 Jul 9, 2021
 #2
avatar+1439 
+2

Let angle BAD = 90º

BD = 5

AX = 2.4

BX = 1.8

DX = 3.2

CX = sqrt(CD2 - DX2

BC = sqrt(BX2 + CX2) = √29

 Jul 10, 2021
 #3
avatar+26122 
+2

Find length BC.


\(\text{Let $BC = \color{red}x$}\)

\(\begin{array}{|lrcll|} \hline (1): & AE^2+DE^2 &=& 4^2 \\ (2): & DE^2+CE^2 &=& 6^2 \\ (3): & AE^2+BE^2 &=& 3^2 \\ (4): & BE^2+CE^2 &=& x^2 \\ \hline \end{array}\)

 

\(\small{ \begin{array}{|lrcll|} \hline (3)-(1)+(2): & (AE^2+BE^2)-(AE^2+DE^2)+ (DE^2+CE^2) &=& 3^2-4^2+6^2 \\ & BE^2+CE^2 &=& 3^2-4^2+6^2 \\ & BE^2+CE^2 &=& 29 \quad | \quad BE^2+CE^2 = x^2 \quad (4) \\ & x^2 &=& 29 \\ & \mathbf{x} &=& \mathbf{\sqrt{29}} \\ \hline \end{array} }\)

 

\(BC = \sqrt{29}\)

 

laugh

 Jul 10, 2021

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