he sum of the length and breadth of a rectangle is 6 cm A square is constructed such that one of its...........

Quantitative Aptitude (CGL) Mensuration 3D

he 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

4√5

10√2

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Explanation:

Let length of rectangle = x
then breadth of rectangel = 6 - x
Area of rectangle = x (6 - x)
Diagonal of rectangle (y)
=√(x^2+(6−x)^2)
=√(x^2+36+x^2−12x)
y=√(2x^2−12x+36)
Now square of side is equal to diagonal.
So, Area of square = y^2
=2x^2−12x+36
2x^2−12x+36x(6−x)=52
4x^2−24x+72=30x=−5x2
9x^2−54x+72=0
9x^2−18x−36x+72=0
9x(x−2)−36(x−2)
9x(x−2)−36(x−2)
(x−2)(9x−36)=0
x=2,x=4
We get two value
By putting x = 2 and x = 4 in Area of square
2x^2−12x+36
we get the area =20cm²