Question

In the rectangular solid in Figure 1, calculate the distance from vertex $A$ to vertex $B$.

• A. $\sqrt{65}$
• B. $7\sqrt{2}$
• C. $9$
• D. $11$

Answer 1

The correct option is C $9$

The length of the diagonal of the bottom face be $BC$.

$\therefore BC=\sqrt{4^2+7^2}$

In $△ABC,$
$A{B}^2=A{C}^2+B{C}^2$

${AB}^2=4^2+(4^2+7^2)$
$AB=\sqrt{16+16+49}$
$=\sqrt{81}$
$\therefore AB=9$