We will begin solving the question by sketching the image to solve the question
Given:
The length of the rectangle is 5 meters longer than the width
The area of the rectangle is 126 square meters
This means that L=5+w
We will use the relationship:
[tex]\text{Area}=\text{length}\times width[/tex][tex]\begin{gathered} \text{Area}=(w+5)w=126 \\ \text{simplifying} \\ w^2+5w=126 \\ w^2+5w-126=0 \end{gathered}[/tex]Simplifying further
[tex]w^2+14w-9w-126=0[/tex][tex]\begin{gathered} w(w+14)-9(w+14)=0 \\ (w+14)(w-9)=0 \end{gathered}[/tex][tex]\begin{gathered} w=9 \\ or \\ w=-14 \end{gathered}[/tex]The width can only be positive
so that
width = 9 meters
so that the length will be w+9
Length = w+9 =9 +5 =15
Length =15 meters
Therefore
width = 9 meters
Length = 14 meters
