A garden is shaped like a rectangle with a width 3 times its length (l). What is the simplified expression for the distance between opposite corners of the garden?

Answer 1

Let's say the length of the rectangle is L and the width is 3L.

Now, the distance between opposite corners of a rectangle can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

So, in this case, the distance between opposite corners can be calculated as:

Distance = √(L^2 + (3L)^2)
Distance = √(L^2 + 9L^2)
Distance = √(10L^2)
Distance = √10 * L

Therefore, the simplified expression for the distance between opposite corners of the garden is √10L.