Diagonals: Using additional geometric shapes

In a rectangle, each pair of opposite sides are equal to each other, therefore:

$AB=DC=4$

We will use the Pythagorean theorem to find AC:

$AC^2=BC^2+DC^2$

Let's substitute the known data:

$AC^2=3^2+4^2$

$AC^2=9+16$

$AC^2=25$

Let's take the square root:

$AC=\sqrt{25}=5$

We will use the Pythagorean theorem in order to find BD:

$BD^2=AD^2+AB^2$

Let's input the known data:

$BD^2=3^2+4^2$

$BD^2=9+16$

$BD^2=25$

We'll take the square root:

$BD=\sqrt{25}=5$