Which one of the following solution is correct for the given geometric representation?

36 x^{2} + 25^{2} + 60 x

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36 x^{2} + 25^{2} - 60 x

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2 (6 x - 5)

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25 (6 x - 5)

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Solution

The correct option is B $36 x^{2} + 25^{2} - 60 x$
Area of yellow square $I D E O =$ Area of square $A C D F$ $-$ Area of rectangle $G O F E$ $-$ Area of rectangle $B C I O$ $-$ Area of red square $A B O G$
Therefore, $(6 x - 5)^{2} = (6 x)^{2} - 5 (6 x - 5) - 5 (6 x - 5) - (5)^{2}$
$=$ $36 x^{2} - 30 x + 5^{2} - 30 x + 5^{2} - 5^{2}$
$=$ $36 x^{2} + 5^{2} - 60 x$
Hence, the second option is the solution for the given geometrical representation $(6 x - 5)^{2} = 36 x^{2} + 25^{2} - 60 x$

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