In order for Mateo to walk 1000 meters in his rectangular backyard, he must walk the length 25 times or the perimeter 10 meters. What is the are of his backyard in square meters?
Thanks!
"perimeter 10 meters "
I guess maybe you mean ten times but it is still nonsense
1000 = 25 L so L = 40 m
1000 = 10 ( L+w)
100 = 40 + w
so w = 60
area = L * w
obviously there is something wrong. width bigger than length
its supposed to be 10 times
To find the area of Mateo's rectangular backyard in square meters, we need to know either the length or the width of the rectangle.
Let's consider the two possibilities given in the question:
1. If Mateo walks the length 25 times to cover 1000 meters, it means the length of the backyard is 1000 / 25 = 40 meters.
2. If Mateo walks the perimeter 10 times to cover 1000 meters, it means the length + width of the backyard is 1000 / 10 = 100 meters.
Since we don't have enough information to determine the specific dimensions of the rectangle, we can only calculate the minimum possible area and the maximum possible area.
Minimum possible area:
If the length of the rectangle is 40 meters, then we need to find the width. Since we know the perimeter (10 meters) is given by the formula: 2 * (length + width), we can substitute the given values: 10 = 2 * (40 + width) and solve for the width. Simplifying the equation, we get 20 + width = 5, and thus, width = 5 - 20 = -15. Since a negative width doesn't make sense, we disregard this value.
Maximum possible area:
If the length + width of the rectangle is 100 meters, we can again use the perimeter formula to find the width. Substituting the given values: 10 = 2 * (100 + width), we simplify the equation to 20 + width = 5, and hence, width = 5 - 20 = -15. Discarding this negative value, we find that the width cannot be derived.
Therefore, with the given information, it is not possible to determine the exact area of Mateo's backyard. We can only conclude that it lies between the minimum and maximum possible areas.