Question

1. the area of a rectangle is 84 square meters. if the length of the rectangle is 5 m longer than its width, find the dimensions. let w be the width of the rectangle in meters. 3a first find the width of the rectangle by solving for w. enter your next step here

Explanation:

Step1: Set up the equation

The area of a rectangle is \(A = length\times width\). Given \(width = w\) and \(length=w + 5\), and \(A = 84\). So, \(w(w + 5)=84\).
Expanding gives \(w^{2}+5w-84 = 0\).

Step2: Factor the quadratic equation

We need to find two numbers that multiply to \(- 84\) and add up to \(5\). The numbers are \(12\) and \(-7\).
So, \((w + 12)(w-7)=0\).

Step3: Solve for \(w\)

Using the zero - product property:
If \(w + 12=0\), then \(w=-12\) (rejected since width cannot be negative).
If \(w - 7=0\), then \(w = 7\).

Answer:

The width of the rectangle is \(7\) meters.