Mathematics

Find the area and the perimeter of a square whose diagonal is 10 cm long.

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Let each side of square be a cm.

Since, sides of square are perpendicular to each other,

In right angle △ABC,

By pythagoras theorem,

⇒ AC² = AB² + BC²

⇒ 10² = a² + a²

⇒ 100 = 2a²

⇒ a² = 50

⇒ a = $\sqrt{50} = 5\sqrt{2}$ cm.

Perimeter = 4a = $20\sqrt{2}$ cm.

Area = a² = 50 cm².

Hence, perimeter = $20\sqrt{2}$ cm and area = 50 cm².

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