Question

What is the approximate side length of the square if the diagonal is 3?

Answer 1

Answer:

Step-by-step explanation:

The diagonal of a square is the same thing as the hypotenuse of a right triangle.  This right triangle is a 45-45-90 since the sides are made up of sides of a square which all measure the same length, x.

Using Pythagorean's Theorem,

$x^2+x^2=3^2$  and

$2x^2=9$  and

$x^2=\frac{9}{2}$  and taking the square root of both sides gives us that

$x=\frac{\sqrt{9} }{\sqrt{2} }$  which simplifies to

$x=\frac{3}{\sqrt{2} }$  I'm assuming that your teacher has told you about rationalizing the denominator when you've got a radical there, so we will do that by multiplying by  $\frac{\sqrt{2} }{\sqrt{2} }$ :

$x=\frac{3}{\sqrt{2} }*\frac{\sqrt{2} }{\sqrt{2} }$  which gives us

$x=\frac{3\sqrt{2} }{2}$