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?

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Solution

Let the side of the original square be x cm and of the small square which is cut off from the original square be y cm.

Sum of the length of all the edges of the original square = 52 cm

⇒ 4x = 52

⇒ x = 13

∴ Length of each side of the original square = 13 cm

According to the question:

Area of resulting figure = 65 cm²

⇒ x² − y² = 65

⇒ (13)² − y² = 65

⇒ 169 − y² = 65

⇒ y² = 104

⇒ y =

∴ Length of each side of the small square = cm

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