Question

$\text{If the side of square is}\frac{1}{2}(x+1)\text{and its diagonal is}\frac{3-x}{\sqrt{2}}\text{units, find the length of a side of the square.}$

• A. 1
• B. 2
• C. 3
• D. 4
• E. 5

Answer 1

The correct option is A

1

$\text{Given side of the square}=\left(\frac{x+1}{2}\right)\text{units and diagonal}=\frac{3-x}{\sqrt{2}}units\text{Also we know diagonal}=\sqrt{2}side\Rightarrow \frac{3-x}{\sqrt{2}}=\sqrt{2}\left(\frac{x+1}{2}\right)\Rightarrow 3-x=2\left(\frac{x+1}{2}\right)\Rightarrow 3-x=x+1\Rightarrow 2x=2\Rightarrow x=1\therefore \text{Length of side}=\frac{x+1}{2}=1unit$