Question

Find the diagonal of a square whose side is 16cm.

Answer 1

Hint: Use the fact that the length of a diagonal of a square with side ‘a’ is given by $\sqrt{2}a$. Substitute the value of the given length of the side of the square and simplify the expression to calculate the length of diagonal of the square.

Complete step-by-step solution -
We have to calculate the length of the diagonal of a square whose side is of length 16cm.
To calculate the length of diagonal of the square, multiply the length of the side of the square by the square root of 2. Thus, the length of a diagonal of a square with side ‘a’ is given by $\sqrt{2}a$.

Substituting $a=16$ in the above expression, the length of diagonal of the square whose side is of length 16cm is $=16\sqrt{2}cm$.
Hence, the length of diagonal of the square whose side is of length 16cm is $16\sqrt{2}cm$.

Note: One must be careful about units while calculating the length of the diagonal of the square. As the length of the side of the square is given in centimetres, the length of diagonal of the square is in centimetres as well. We must know that as all the sides of a square are of equal length, the length of both the diagonals is equal as well. Diagonals of a square cross each other at an angle of ${{90}^{\circ }}$. Thus, they are perpendicular bisectors of each other.