Question

Length of the diagonal AC of a square ABCD is 10 cm. Find the length of each side of the square

• A. $7.07cm$
• B. $6.05cm$
• C. $8cm$
• D. $9.12cm$

Answer 1

The correct option is A $7.07cm$

$AC=10cm$
We know that all sides of a square are equal.
$\therefore AB=BC=CD=DA$
And each angle measures ${90}^o$.
$\therefore \angle ABC=\angle BCD=\angle CDA=\angle DAB={90}^o$
Now, in right angles $\Delta ABC$
$A{C}^2=A{B}^2+B{C}^2$
(By Pythagorean theorem)
$\Rightarrow {10}^2=A{B}^2+A{B}^2$
$\Rightarrow 100=2A{B}^2$
$\Rightarrow \frac{100}{2}=A{B}^2$
$\Rightarrow A{B}^2=50$
$AB=\sqrt{50}=7.07(approx.)$
Since all the sides of a square are equal, therefore, $AB=BC=CD=DA=7.07cm(approx.)$