Question

Four congruent rectangles are place as shown in the figure. Area of the outer square is 4 times that of the inner square is 4 times that of the inner square. What is the ratio of length to breadth of the congruent rectangles?

Answer 1

Let the side length of the smaller square be 1,

and let the smaller side of the rectangles be y.

Since the larger square's area is four times

larger than the smaller square's, the larger

square's side length is 2. That too is then

equivalent to 2y + 1 , giving y = 1 /2 . Then, the

larger piece of the rectangles is 3 / 2 , 3/2 , 1 / 2

= 3 Answer

ratio is 3 : 1

if it's help you then don't forget to follow me

Answer 2

Solution :

Let the side of outer square = s ---( 1 )

side of the inner square = a ----( 2 )

According to the problem given ,

Area of the outer square = 4 × area of the

inner square

=> s² = 4a²

=> s = √( 2a )²

=> s = 2a ----( 3 )

Now ,

Let the breadth of the each congruent

rectangle = b

Side of outer square = s

=> b + a + b = s

=> 2b + a = s

=> 2b = s - a

=> b = ( s - a )/2

= ( 2a - a )/2

= a/2 ---- ( 4 )

Length of each congruent rectangle

( l ) = s - b

= 2a - a/2

= ( 4a - a )/2

= 3a/2

Therefore ,

Ratio = l : b

= ( 3a/2 )/( a/2 )

= 3 : 1

•••••