Question : The sum of the length and breadth of a rectangle is 6 cm. A square is constructed such that one of its sides is equal to a diagonal of the rectangle. If the ratio of areas of the square and rectangle is 5 : 2, the area of the square (in cm2) is:
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution :
Let the length of the rectangle as
Given that the sum of the length and breadth of the rectangle is 6 cm.
The diagonal
Given that the ratio of the areas of the square and the rectangle is 5 : 2,
Substituting equation (2) into equation (3),
Solving equations (1) and (4) simultaneously,
⇒
⇒
Taking
Substituting these values into equation (2),
The area of the square,
Hence, the correct answer is
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