Respuesta :

LammettHash
The diagonal of any square always occurs in a ratio of [tex]\sqrt2:1[/tex] relative to the square's sides. That means if [tex]s[/tex] is the side length, then [tex]\sqrt2s=8[/tex] gives the length of the diagonal. It follows that [tex]s=\dfrac8{\sqrt2}[/tex].

Then the area of the square is

[tex]s^2=\left(\dfrac8{\sqrt2}\right)^2=\dfrac{64}2=32[/tex] square inches
If you look carefully, that diagonal would be the Hypotenuse and the arms of the Square (which is equal in magnitude) would be the shorter sides.

Then, According to Pythagoras Theorem, 
a² + b² = c²
2a² = 8²
a² = 64/2
a = √32

Now, Area = Side²

So, A = (√32)²
A = 32 in²

In short, Your Answer would be; 32 in²

Hope this helps!

Otras preguntas