Final answer:
To find the width of the rectangle with the given area and the relationship between length and width, we set up a quadratic equation from the area formula. After solving the quadratic equation, we get two potential values, of which the positive value is the actual width of 7 meters.
Step-by-step explanation:
The student asked to find the width of a rectangle where the length is 5 meters longer than the width, and the area of the rectangle is 84 m². To calculate the width, let the width be represented by 'w' meters. Therefore, the length will be 'w + 5' meters. The area of a rectangle is found by multiplying the length and width, so the equation is:
w × (w + 5) = 84
Expanding this equation gives:
w² + 5w - 84 = 0
This is a quadratic equation that can be factored into:
(w - 7)(w + 12) = 0
Setting each factor equal to zero gives us two potential solutions for 'w':
w = 7 or w = -12
Since a width cannot be negative, the width must be 7 meters.
Therefore, the width of the rectangle is 7 meters.