Problem 36 - Introductory Algebra for College Students

Question

A basketball court is a rectangle with a perimeter of 86 meters. The length is 13 meters more than the width. Find the width and length of the basketball court.

Step-by-Step Solution

Answer

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

Step 1: Setup the equations

You can setup two relations between the dimensions of the court: one is generated by the definition of the perimeter of a rectangle \(P = 2L + 2W\), the other one is given by the problem \(L = W + 13\).

Step 2: Substitute in the First equation

Plug in \(L = W + 13\) meters into the perimeter equation: \(P = 2(W + 13) + 2W\). Normally, you would substitute the value of the perimeter as well, but in this case leaving \(P\) as a variable is useful to check the solution later.

Step 3: Solve for W

The equation from Step 2 simplifies to \(P = 4W + 26\). Now, substitute the given value for the perimeter \(P = 86\) and simplify to solve for \(W\), the court's width. \(86 = 4W + 26\).

Step 4: Calculate W

Subtract 26 from both sides of the equation and then divide by 4: \(W = (86 - 26) / 4 = 15\) meters.

Step 5: Calculate L

Substitute \(W = 15\) meters into \(L = W + 13\) to find the court's length. \(L = 15 + 13 = 28\) meters.