A square and a triangle have equal areas. If the ratio side of square and the height of triangle is 2/3 . Find the ratio of base to height. Is its answer 9/8 or 8/9?

Answer :

Given :  Ratio of side of square :  Height of triangle  =  2  :  3

And area of square  =  Area of triangle

Let ratio coefficient  =  x , So

Side of square  =  2x  and

Height of triangle =  3x 

And we know 

Area of square  =  ( Side ) ( Side )

And

Area of triangle  = 12 (  Base ) ( Height )

So, we get from given condition that area of square is equal to the area of triangle  , So

( Side ) ( Side )  = 12 (  Base ) ( Height ) 
Substitute values , we get

( 2x ) ( 2x ) = 12 (  Base ) ( 3x )

Base =  8x3 , So

BaseHeight = 8x33x  = 8x9x    = 89         ( Ans )
 

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