#### Answer

The length of the basketball court is $28$ meters and the width is $15$ meters.

#### Work Step by Step

The perimeter of a rectangle is given by the following formula.
$$P = 2l + 2w$$
We know that the perimeter of the basketball court is $86$ meters. So we can substitute this for $P$.
$$86 = 2l + 2w$$
If the length is $13$ meters more than the width, we want to set the width as $w$ and the length as $w + 13$. We can now plug these into the equation to find the perimeter:
$$86 = 2(w + 13) + 2(w)$$
We now simplify the equation:
$$2w + 26 + 2w = 86$$
We combine like terms:
$$4w + 26 = 86$$
We subtract $26$ from both sides:
$$4w = 60$$
We now solve for $w$:
$$w = 15$$
We can now solve for the length because we know that the length is $w + 13$.
$$l = w + 13$$
Plug in $15$ for $w$:
$$l = 15 + 13$$
Solve for $l$:
$$l = 28$$
The length of the basketball court is $28$ meters and the width is $15$ meters.