A rectangular parcel of land has an area of 4,000 ft2. A diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel. What are the dimensions of the land, correct to the nearest foot?

Question

A rectangular parcel of land has an area of 4,000 ft2. A diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel. What are the dimensions of the land, correct to the nearest foot?

Answer 1

if the side is x, then the other side is 4000/x. So, we have

x^2 + (4000/x)^2 = (x+10)^2
x â‰ˆ 91

check:
the rectangle is about 91x44
The diagonal is 101 = 91+10

Answer 2

To find the dimensions of the land, we can set up a system of equations based on the given information.

Let's assume the length of the rectangular parcel is L feet and the width is W feet.

We are given that the area of the land is 4,000 ft^2, so we have the equation:
L * W = 4000 ...............(1)

We are also given that the diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel. The diagonal forms a right triangle with the length and width of the land. Using the Pythagorean theorem, we can write the equation for the diagonal as:
√(L^2 + W^2) = L + 10 ...............(2)

Now, we can solve this system of equations to find the values of L and W.

We can start by isolating L in equation (2):
√(L^2 + W^2) - 10 = L

Next, we can substitute this expression for L into equation (1):
(√(L^2 + W^2) - 10) * W = 4000

Expanding the equation and simplifying, we get:
W*√(L^2 + W^2) - 10W = 4000

Now, we can square both sides of equation (2) to eliminate the square root:
L^2 + W^2 = (L + 10)^2

Simplifying this equation, we get:
L^2 + W^2 = L^2 + 20L + 100

Subtracting L^2 from both sides and rearranging the equation, we have:
W^2 = 20L + 100 ...............(3)

Now, we can substitute equation (3) into the expanded equation (W*√(L^2 + W^2) - 10W = 4000):
(20L + 100)*√(L^2 + W^2) - 10W = 4000

Dividing the entire equation by 10, we get:
2(2L + 10)√(L^2 + W^2) - W = 400

Now, let's solve this equation using numerical methods or a calculator:

By substituting different values for L and W, we can solve for the dimensions until the left side of the equation is nearly equal to 400 (to the nearest foot). As an AI text-based bot, I suggest using a numerical method or a calculator for quicker and more accurate results.