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Let be:
b: side of the small square to the left of the square of side 1.

We can deduce the dimensions of the rectangle:
\(left side = 5b + 1\)
\(botton side = 4b + 3\)
\(right side = 3b + \frac{7}{2}\)

As left side must be equal to right side:
\(5b + 1 = 3b + \frac{7}{2}\) -> \(b = \frac{5}{4}\)

Area of rectangle:
\((5b + 1)(4b + 3) = \frac{29}{4} * 8 = 58\)

IMO E
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If we look at the attached figure.

Let AB = x ;

On the basis of properties of square, other side dimensions in term of x are given

Now let consider the shaded square,

one side comes to 2x -3, but the other one comes to 8 - 2x .

Since both are equal,

2x - 3 = 8 - 2x

or 4x = 11
or x = 11/4

Area = ( 4x -3) (3x - 1)
= ( 11 -3) ( 33/4 - 1)
= 8 * 7.25
= 58
So option E is correct
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Q : Rectangle given above is divided into eight square

Answer : E

if we divide the total rectangle as shown in the figure,
we end with the equation :
(6 + 5x)(7 + 4x) , since area of rectangle = (length)*(breadth)

and here length = 7 + 2x
breadth = 6 + 4x
where x >0

solving the equation gives us : 42 + 20x^2 + 79x, which is always greater than 42 and hence only option greater than 42 is E

#Geometry
#Quant
#700
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