Question

In a square ABCD, the length of diagonal, AC is 10 cm. Find the length of the diagonal, BD.

Answer 1

Assume, side of the square is ‘a’ units.

Also, we know that in a square measure of each angle is 90°.
So, triangle ABC forms a right angled triangle.
We know that in a right angled triangle
$hypotenus{e}^2=sid{e}^2+sid{e}^2$
$A{C}^2=A{B}^2+B{C}^2$
$A{C}^2=a^2+a^2$
$A{C}^2=2a^2$
$AC=a\surd 2$ cm -- (i)

Now; draw the diagonal BD
Triangle ABD is a right angled triangle
$hypotenus{e}^2=sid{e}^2+sid{e}^2$
$B{D}^2=A{B}^2+A{D}^2$
$B{D}^2=a^2+a^2$
$B{D}^2=2a^2$
$BD=a\surd 2$ cm -- (ii)

From (i) and (ii) we got
$AC=BD=a\surd 2$ cm -- (iii)

Since, it is given that, the length of the diagonal AC is 10 cm.
So, from (iii); the length of diagonal BD = 10 cm.