What are the dimensions of a rectangular tract of land if its perimeter is 70 kilometers and its area is 300 square kilometers?
km (smaller value)
akm (larger value)
hey r u single
2 w + 2 L = 70 so w+L = 5 and L = (35-w)
300 = w (35-w)
w^2 -35 w + 300 = 0
(w-20)(w-15) = 0
w = 15 or 20
so
w = 15 and L = 20
To determine the dimensions of a rectangular tract of land, given its perimeter and area, you need to use the formulas for perimeter and area of a rectangle.
The perimeter of a rectangle can be calculated by adding the lengths of all four sides. In this case, the perimeter is given as 70 kilometers.
Let's assume the length of the rectangle as "l" kilometers and the width as "w" kilometers. Since there are two lengths and two widths in a rectangle, we can express the perimeter as:
Perimeter = 2l + 2w = 70 kilometers
The area of a rectangle is found by multiplying the length and width. In this case, the area is given as 300 square kilometers:
Area = l * w = 300 square kilometers
Now, we can use these equations to solve for l and w.
From the equation 2l + 2w = 70, we can rewrite it as:
l + w = 35
We can rearrange this equation to express l in terms of w as:
l = 35 - w
Substituting this expression for l into the equation for area, we have:
(35 - w) * w = 300
Expanding and rearranging this equation, we get:
w^2 - 35w + 300 = 0
We can solve this quadratic equation to find the values for w (width) which will then help us find the corresponding values for l (length).
Solving for w, we find two possible values: w = 20 and w = 15.
If we take w = 20, we can substitute this back into the equation l + w = 35:
l + 20 = 35
l = 35 - 20
l = 15
Therefore, the dimensions of the rectangular tract of land can be expressed as:
Width (smaller value) = 15 kilometers
Length (larger value) = 20 kilometers