Question

Six squares are connected such that two squares share only one side. Then what is the shortest distance between two opposite corners given that the side length of the square is a?

• A. $\sqrt{\frac{5}{2}}a$
• B. $\sqrt{3}a$
• C. $a$
• D. $\sqrt{2}a$

Answer 1

The correct option is B

$\sqrt{3}a$

The shortes distance between A and D will a line joining A and D.

Using Pythagoras theorem $\Delta ABC$

$A{C}^2=A{B}^2+B{C}^2$

$AC=\sqrt{2}a$

Using Pythagoras theorem in $\Delta ACD$

$A{D}^2=A{C}^2+C{D}^2$

$AD=\sqrt{3}a$