Question

The length of diagonal of a square is 10√2 cm. Find its side.

Answer 1

➲ It is given in the question that length of diagonal of a square is 10√2 cm.

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» Let each side of the square be x cm.

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As we can see in the figure that ABC is a right angled triangle, with hypotenuse AC.

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[According to Pythagoras theorem]

• In a right angled triangle, square of Hypotenuse is equal to the sum of the square of the other two sides.

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$\: \: \: \: \: \: \: \: \: \:\underline{\bf{\red{AC^2 = AB^2 + BC^2}}}$

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$\tt:\implies{(10 \sqrt{2})^2 = x^2 + x^2}$

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$\tt:\implies{200 = 2x^2}$

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$\tt:\implies{x^2 = \dfrac{200}{2}}$

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$\tt:\implies{x^2 = 100}$

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$\tt:\implies{x = \sqrt{100}}$

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$\frak:\implies{\pink{x = 10}}$

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Hence, each side of the square is of 10cm.