Question

a rectangle has a perimeter of 30 feet and an area of 50 square feet. what is the length, in feet, of the longest side of the rectangle? 7 8 9 10

Explanation:

Step1: Set up equations

Let the length be \(l\) and the width be \(w\).
Perimeter formula: \(2(l + w)=30\), so \(l + w = 15\), then \(w=15 - l\).
Area formula: \(lw = 50\).

Step2: Substitute and solve

Substitute \(w = 15 - l\) into \(lw = 50\):
\(l(15 - l)=50\)
\(15l-l^{2}=50\)
\(l^{2}-15l + 50=0\)
Factor: \((l - 10)(l - 5)=0\)
So \(l=10\) or \(l = 5\).

Answer:

10