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The sum of the areas of two similar polygons is 65 square units. If their perimeters are 12 units and 18 units, respectively, what is the area of the larger polygon?

 Jul 3, 2020
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The areas of similar polygons have the same ratio as the squares of the corresponding sides.

[Perimeters count as lengths.]

 

Since Area ( polygon A )  +  Area( p0lygon B )  =  65     --->     Area( polygon B )  =  65  -  Area( polygon A )

 

Area( polygon A) : Area( polygon B )  =  Perimeter( polygon A )2 : Perimeter( polygon B )2 

Area( polygon A) : [ 65 - Area( polygon A ) ]  =  12 : 18

 

To make the algebra easier, call Area( polygon A ) = x

 

--->   x : ( 65 - x )  =  12 : 18     

 

Cross-multiply:  12( 65 - x )  =  18x

                            780 - 12x  =  18x

                                     780  =  30x

                                          x  =  26

--->   65 - x  =  65 - 26  =  39

 Jul 3, 2020

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