Question

a rectangle has a perimeter of 24 feet and an area of 27 square feet. what is the length, in feet, of the longest side of the rectangle?
3
4.5
6
9

Explanation:

Step1: Set up equations

Let the length be \(l\) and the width be \(w\).
Perimeter formula: \(2(l + w)=24\), so \(l + w = 12\), then \(w=12 - l\).
Area formula: \(lw = 27\).

Step2: Substitute and solve

Substitute \(w = 12 - l\) into \(lw = 27\):
\(l(12 - l)=27\)
\(12l-l^{2}=27\)
\(l^{2}-12l + 27=0\)
Factor: \((l - 3)(l - 9)=0\)
So \(l=3\) or \(l = 9\).

Answer:

\(9\)