find x in this rectangle

**beq!x** · April 3rd 2009, 01:37 PM

in a Rectangle
distance AE= 14 m , DE=4 m, CE=12 M
find BE=X=?

**red_dog** · April 3rd 2009, 02:26 PM

Let $EM\perp AD, \ EN\perp DC, \ EP\perp BC, \ EQ\perp AB$

$EM=a, \ EN=b, \ EP=c, \ EQ=d$

Then,

$a^2+b^2=16$ (1)

$b^2+c^2=144$ (2)

$c^2+d^2=x^2$ (3)

$d^2+a^2=196$ (4)

(1)+(3) $\Rightarrow a^2+b^2+c^2+d^2=x^2+16$

(2)+(4) $\Rightarrow a^2+b^2+c^2+d^2=340$

$\Rightarrow x^2+16=340\Rightarrow x^2=324\Rightarrow x=18$

**beq!x** · April 4th 2009, 04:37 AM

yes it is right, x=18 i have solved this today at school. thanks however .

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