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Q.

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

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a

102

b

45

c

10

d

20

answer is A.

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Detailed Solution

Let length of rectangle = x then, 

Breath of rectangle = (6 - x)

Side of square= diagonal of rectangle. 

Let area of square = 5x 

Now,

x2+(6x)2=5x2x217x+36=02x29x8x+36=0x(2x9)4(2x9)

(x4)(2x9)x4=0 x=42x9=0 x=9/2

Take x = 4; then,

 Area of square =5x=5×4=20 cm2.

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