A rectangular lot is surrounded by a rock wall 46 meters in length. What are the dimensions of the lot if its length is 5 meters longer than its width
P = 2L + 2W
46 = 2(W + 5) + 2W
46 = 2W + 10 + 2W
46 - 10 = 4W
36 = 4W
? = W
To find the dimensions of the lot, we can use the given information and set up an equation. Let's assume that the width of the lot is "W" meters.
Since the length of the lot is 5 meters longer than its width, we can express the length as "W + 5" meters.
According to the problem, the rock wall surrounds the rectangular lot, which means all four sides of the lot (two lengths and two widths) must add up to the total length of the wall, which is 46 meters.
So, we can set up the equation as follows:
2(W + 5) + 2W = 46
Simplifying the equation:
2W + 10 + 2W = 46
4W + 10 = 46
4W = 46 - 10
4W = 36
Dividing both sides of the equation by 4:
W = 36 / 4
W = 9
Therefore, the width of the lot is 9 meters.
To find the length, we can substitute the value of the width into the expression we found earlier:
Length = Width + 5
Length = 9 + 5
Length = 14
So, the dimensions of the lot are 14 meters by 9 meters.