A corner lot that originally was square lost 185 m of area when one of the adjacent streets was widened by 3 m and the other was widened by 5 m. Find the new dimensions of the lot.
To find the new dimensions of the lot, we can use the information given.
Let's assume that the original length and width of the lot were both x meters, making it a square.
The original area of the lot is given by x^2 square meters.
When one of the adjacent streets was widened by 3 m and the other by 5 m, the new length would be x + 5 meters and the new width would be x + 3 meters.
We know that the new area of the lot is the original area minus 185 square meters. So, we can set up the equation:
x^2 - 185 = (x + 5)(x + 3)
Expanding the right side of the equation, we get:
x^2 - 185 = x^2 + 8x + 15
Simplifying the equation, we get:
8x + 15 = 185
Subtracting 15 from both sides, we get:
8x = 170
Dividing both sides by 8, we get:
x = 21.25
Therefore, the original length and width of the lot were both 21.25 meters.
The new length of the lot is: 21.25 + 5 = 26.25 meters
The new width of the lot is: 21.25 + 3 = 24.25 meters
So, the new dimensions of the lot are 26.25 meters by 24.25 meters.
To find the new dimensions of the lot, we can start by assuming the original dimensions of the square lot were x by x.
When one of the adjacent streets was widened by 3 m, the length of the lot would increase by 3 m, while the width would remain the same. This would result in the dimensions becoming (x + 3) by x.
Similarly, when the other adjacent street was widened by 5 m, the length of the lot would increase by 5 m, and again the width would remain the same. This would result in the dimensions becoming (x + 3) by (x + 5).
Now, we need to calculate the area of the original square lot and the new area after the streets were widened.
Original area of the square lot = x * x = x^2
New area of the lot after widening the streets = (x + 3) * (x + 5)
According to the problem, the new area is 185 m² less than the original area. So, we can set up the equation:
(x + 3) * (x + 5) = x^2 - 185
Expanding the equation:
x^2 + 5x + 3x + 15 = x^2 - 185
Combining like terms:
x^2 + 8x + 15 = x^2 - 185
Subtracting x^2 from both sides:
8x + 15 = -185
Subtracting 15 from both sides:
8x = -200
Dividing by 8:
x = -25
Since the length and width cannot be negative, this result is not applicable.
Therefore, there might be an error in the problem or some missing information.