Question

homework assignment 7.3 systems of nonlinear equations and in
score: 6/16 answered: 6/16
question 7
a rectangle has an area of 180 cm² and a perimeter of 58 cm.
what are its dimensions?
its length is cm
its width is cm, where length > width
question help: video read written example

Explanation:

Step1: Set up equations

Let the length be \( l \) and the width be \( w \).
The area formula: \( lw = 180\).
The perimeter formula: \(2(l + w)=58\), so \(l + w = 29\), then \(l=29 - w\).

Step2: Substitute and solve

Substitute \(l = 29 - w\) into \(lw = 180\):
\((29 - w)w=180\)
\(29w-w^{2}=180\)
\(w^{2}-29w + 180=0\)
Factor: \((w - 9)(w - 20)=0\)
So \(w = 9\) or \(w = 20\).
If \(w = 9\), then \(l=29 - 9=20\).
If \(w = 20\), then \(l=29 - 20 = 9\). But since \(l>w\), we take \(l = 20\) and \(w = 9\).

Answer:

Its length is \(20\) cm.
Its width is \(9\) cm.