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What is the perimeter, in cm, of quadrilateral $ABCD$ if $\overline{AB} \perp \overline{BC}$, $\overline{DC} \perp \overline{BC}$, $AB=9$ cm, $DC=4$ cm, and $BC=12$ cm?

 Mar 19, 2020
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  A         9                B

 

                              12

 

         D          4       C

 

Let A  = (0,0)

Let B= (9,0)

Let C = ( 9, -12)

Let D = (5, -12)

 

We know  three sides......we  just need to find AD  =  sqrt [ ( 0 - 5)^2 + ( -12 - 0)^2 ] =

 

sqrt [ (-5)^2  + (-12)^2 ]  =

 

sqrt [ 25  + 144 ] =

 

sqrt [ 169]  =

 

13

 

So.....the perimeter is    9 + 12 + 4 + 13   =   38 cm

 

 

cool cool cool

 Mar 20, 2020
edited by CPhill  Mar 20, 2020

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