Question

A square has sides $s$ and diagonal $d$. If $2s^2+d^2=100$, what is the value of $s$?

• A. $3$
• B. $5$
• C. $10$
• D. $25$

Answer 1

The correct option is B $5$

Here, $ABCD$ is a square.

$AB=BC=CD=DA=s$ and $AC=d$

$2s^2+d^2=100$ [ Given ]

$\therefore$ $d^2=100-2s^2$ ----- ( 1 )

In right angle $△ABC,$

$\Rightarrow$ $(AC{)}^2=(AB{)}^2+(BC{)}^2$ [ By Pythagoras theorem ]

$\Rightarrow$ $d^2=s^2+s^2$

$\Rightarrow$ $100-2s^2=2s^2$ [ From ( 1 ) ]

$\Rightarrow$ $100=4s^2$

$\Rightarrow$ $s^2=25$

$\therefore$ $s=5$