The length of a rectangle is 2 meters more than its width. If the area is 35 square meters, what are the length and width?
5 meters by 7 meters
a rectangular parking lot has a length that is 6 yards greater than the width. The area of the parking lot is 160 square yards. find the length and the width.
To find the length and width of the rectangle, we can use the information given in the problem. We are told that the length of the rectangle is 2 meters more than its width. Let's assume that the width of the rectangle is "W".
So, according to the problem, the length of the rectangle would be "W + 2" meters.
The formula to find the area of a rectangle is as follows:
Area = Length × Width
Since we are given that the area is 35 square meters, we can substitute the values into the formula:
35 = (W + 2) × W
Now we can solve the equation to find the values of "W" and "W + 2".
To do so, let's simplify the equation:
35 = W^2 + 2W
Rearranging the equation in standard quadratic form:
W^2 + 2W - 35 = 0
To solve this quadratic equation, we can factor it or use the quadratic formula. Let's use the quadratic formula, which states:
For an equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
For our equation, a = 1, b = 2, and c = -35. Plugging these values into the quadratic formula:
W = (-2 ± sqrt(2^2 - 4(1)(-35))) / (2(1))
Simplifying further:
W = (-2 ± sqrt(4 + 140)) / 2
W = (-2 ± sqrt(144)) / 2
W = (-2 ± 12) / 2
Now, we have two possible solutions for W:
1. When W = (-2 + 12) / 2 = 10 / 2 = 5
2. When W = (-2 - 12) / 2 = -14 / 2 = -7
Since the width of a rectangle cannot be negative, we discard the second solution. Therefore, the width of the rectangle is 5 meters.
To find the length, we can use the equation:
Length = Width + 2
Substituting the value of the width we just found:
Length = 5 + 2 = 7
So, the length of the rectangle is 7 meters and the width is 5 meters.