Question

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

Answer 1

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=(9)/(2)` and taking the square root of both sides gives us that

`x=(√(9) )/(√(2) )` which simplifies to

`x=(3)/(√(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
`(√(2) )/(√(2) )` :

`x=(3)/(√(2) )*(√(2) )/(√(2) )` which gives us

`x=(3√(2) )/(2)`