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Question

It is possible to construct a square if only one of its diagonals is given.


A

Yes

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B

No

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Solution

The correct option is A

Yes


If the length of diagonal of a square is known, we can find out the length of the side of the square. For e.g.

If diagonal length is 'a' in ABC, using Pythagoras theorem

AB2+ BC2= AC2

x2+x2= a2

2x2= a2

x2= a2/2

x=a/2

Now, we know that square is a regular quadrilateral. So, all the sides are equal to each other and all the angles are equal to each other. We hence have total of 8 measurements (4 sides + 4 angles). Hence, it is possible to construct a square if only one of its diagonals is known.

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