Final answer:
The dimensions of the floor with an area of 84 square meters and a length that is 5 meters longer than its width are 7 meters in width and 12 meters in length.
Step-by-step explanation:
The question asks us to determine the dimensions of a floor where the length is 5 meters longer than its width, and the total area is 84 square meters. Let's denote the width of the floor as w meters. Therefore, the length of the floor is w + 5 meters. The area of a rectangle is calculated as length × width, and we can set up the following equation to solve for w:
w(w + 5) = 84
Now, we distribute the w and set up a quadratic equation:
w²+ 5w - 84 = 0
Factoring the quadratic equation, we find that w could be 7 or -12. Since a negative width doesn't make sense in this context, we discard the -12 and accept w as 7 meters. So, the dimensions of the floor are 7 meters in width and 12 meters in length (since 7 + 5 = 12).