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 = ( Base ) ( Height )
So, we get from given condition that area of square is equal to the area of triangle , So
( Side ) ( Side ) = ( Base ) ( Height )
Substitute values , we get
( 2x ) ( 2x ) = ( Base ) ( 3x )
Base = , So
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 = ( Base ) ( Height )
So, we get from given condition that area of square is equal to the area of triangle , So
( Side ) ( Side ) = ( Base ) ( Height )
Substitute values , we get
( 2x ) ( 2x ) = ( Base ) ( 3x )
Base = , So