Question

Is it possible to construct a square if only one of its diagonals is given?

• A. Yes
• B. No
• C. With 4 other measurements, Yes
• D. With the measurement of a side, Yes

Answer 1

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

${AB}^2$+ ${BC}^2$= ${AC}^2$

$x^2$+$x^2$= $a^2$

2$x^2$= $a^2$

$x^2$= $\frac{a^2}{2}$

x= $\frac{a}{\sqrt{2}}$

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. So we 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.