Math Snap

STEP 1

Assumptions1. The length of the rectangular court is9 ft longer than twice the width.
. The perimeter of the court is108 ft.
3. We need to find the length and width of the court.

STEP 2

Let's denote the width of the rectangular court as $w$ (in feet). Then, according to the problem, the length of the court is $2w +9$ (in feet).

STEP 3

The formula for the perimeter of a rectangle is given by $=2l +2w$, where $l$ is the length and $w$ is the width.

STEP 4

We can substitute the values of $l$ and $$ from the problem into the formula for the perimeter. This gives us the equation $108 =2(2w +9) +2w$.

STEP 5

implify the equation.
$$108 =4w +18 +2w$$

STEP 6

Combine like terms.
$$108 =6w +18$$

STEP 7

Subtract18 from both sides of the equation to isolate the term with $w$.
$$108 -18 =6w$$

STEP 8

implify the left side of the equation.
$$90 =6w$$

STEP 9

Divide both sides of the equation by6 to solve for $w$.
$$w =90 /6$$

STEP 10

Calculate the value of $w$.
$$w =15$$

STEP 11

Now that we have the width of the court, we can find the length by substituting $w$ into the equation $l =w +9$.
$$l =(15) +9$$

Calculate the value of $l$.
$$l =30 +9 =39$$The length of the court is39 ft and the width is15 ft.