From the middle of a square, a small square is cut off. The area of the resulting figure is 65 square centimetres and the sum of the lengths of all its edges is 52 centimetres. What is the length of a side of the original square and the square cut off?

my teacher did it in another way juzz remember

and the answer given in this site is wrong

Let the length of the original side be 'x' and the length of the small square be 'y'.

Given the area of the resulting square = 65 cm^2

So,

x^2-y^2=65...(1)

Though the small square is cut off from the middle of the square, still its edges remain same.

So, 4x= 52

x=13

From (1),

13^2-y^2=65

169-y^2=65

y^2=169-65=104

y =√104=2√26 cm

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