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Chapter 2: Problem 36

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.

Short Answer

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

Step by step solution

01

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 \(L = W + 13\).
02

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.
03

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. \(86 = 4W + 26\).
04

Calculate W

Subtract 26 from both sides of the equation and then divide by 4: \(W = (86 - 26) / 4 = 15\) meters.
05

Calculate L

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

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