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.