Certainly! Let's solve the word problem step-by-step.
### Problem
International basketball competitions are played on a rectangular court where:
- The length of the court is 2 meters less than twice the width.
- The perimeter of the court is 86 meters.
We are to find the dimensions (length and width) of the court.
### Step-by-Step Solution
1. Define Variables:
Let \(\( w \)\) be the width of the court in meters.
Let \(\( l \)\) be the length of the court in meters.
2. Translate the Problem Conditions into Equations:
- According to the problem, the length \(\( l \)\) is 2 meters less than twice the width:
\(\[
l = 2w - 2
\]\)
- The perimeter of a rectangle is given by the formula:
\(\[
\text{Perimeter} = 2 \times (\text{length} + \text{width})
\]\)
- The perimeter of the court is given as 86 meters:
\(\[
2(l + w) = 86
\]\)
3. Substitute the Expression for the Length into the Perimeter Equation:
- Using the equation \(\( l = 2w - 2 \)\), substitute \(\( l \)\) into the perimeter equation:
\(\[
2((2w - 2) + w) = 86
\]\)
4. Simplify and Solve for \(\( w \)\):
\(\[
2(2w - 2 + w) = 86
\]\)
\(\[
2(3w - 2) = 86
\]\)
\(\[
6w - 4 = 43
\]\)
\(\[
6w = 45
\]\)
\(\[
w = 7.5
\]\)
So, the width \(\( w \)\) of the court is 7.5 meters.
5. Find the Length \(\( l \)\):
- Substitute \(\( w = 7.5 \)\) back into the expression for the length:
\(\[
l = 2w - 2
\]\)
\(\[
l = 2(7.5) - 2
\]\)
\(\[
l = 15 - 2
\]\)
\(\[
l = 13
\]\)
So, the length \(\( l \)\) of the court is 13 meters.
### Conclusion:
The dimensions of the basketball court are:
- Width: 7.5 meters
- Length: 13 meters
