The diagonal of a square is 8 square root 2 units. Which is the perimeter of the square?
8
16
24
32

Question

The diagonal of a square is 8 square root 2 units. Which is the perimeter of the square?
    8 
   16 
   24 
   32

jim_thompson5910 · Answer

The relationship between the diagonal of the square (d) and the side of the square (s) is given by 

$$d=s\sqrt{2}$$

Solve for 's' to get $$s=\frac{d}{\sqrt{2}}$$


Now plug in d=8 square root of 2 and simplify to find s


$$s=\frac{d}{\sqrt{2}}$$


$$s=\frac{8\sqrt{2}}{\sqrt{2}}$$


$$s=8$$


So the length of the side of the square is 8 units


So the perimeter is 8*4 = 32 units.

anonymous · Answer

Thkank you (:

anonymous · Answer

Alternatively, Pythagorus for the square with side a

8 sqrt 2 = sqrt (2a^2) -> a = 8-> 32.

anonymous · Answer

A trig solution:$$\text{perimeter}=4*8\sqrt{2}\text{Sin}[45{}^{\circ}] $$

anonymous · Answer

Sorry.$$\text{perimeter}=4*8\sqrt{2}\text{Sin}[45{}^{\circ}]=32 $$