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A rectangle is divided into four small rectangles as shown. The areas of three of the four small rectangles are labeled in the diagram. What is the area of the remaining small rectangle?

pls solve quickly! Thanks ;)

off-topic
Guest Oct 3, 2017
edited by Guest  Oct 3, 2017
edited by Guest  Oct 3, 2017
edited by Guest  Oct 3, 2017
edited by Guest  Oct 3, 2017
 #1
avatar+7155 
+2

 

ab  =  4     →     a  =  4 / b

bd  =  3

cd  =  5     →     c  = 5 / d

 

area of remaining rectangle  =  ac  =  \(\frac4b\cdot\frac5d=\frac{20}{bd}=\frac{20}{3}\)

hectictar  Oct 3, 2017
 #2
avatar+87309 
+2

Thanks, hectitctar!!!......there is a sligtly faster way of finding the missing area

 

Using hectictar's diagram [ along with a theorem from Euclid ]

 

        area of ab *  area of dc =   area of bd * area of ac

 

               4        *         5            =         3        *    area of ac

 

                      20                      =          3        *    area of ac      

 

                                Divide both sides by 3

 

 

                                20 / 3   =  area of ac   

 

 

 

cool cool cool  

CPhill  Oct 4, 2017
edited by CPhill  Oct 4, 2017

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