What is the length of the diagonals of the rectangle?round your answer to the nearest hundredth if necessary
To find the length of the diagonals of a rectangle, we can use the Pythagorean theorem. Let's assume the length of the rectangle is L and the width is W.
The length of the diagonal can be found by finding the square root of the sum of the squares of the length and width.
\(\sqrt{L^2 + W^2}\)
Since it's a rectangle, opposite sides are equal in length. Therefore, we can say \(L = W\).
Substituting the values, we have:
\(\sqrt{L^2 + L^2} = \sqrt{2L^2}\)
Simplifying, we get:
\(\sqrt{2L^2} = \sqrt{2}L\)
So, the length of the diagonal of the rectangle is \(\sqrt{2}L\).