Final answer:
To find the dimensions of the rectangular parcel of land, use the equation L * W = 5000 and the Pythagorean theorem equation L² + W² = (L+10)². Solve this system of equations to find that the width is approximately 25 ft and the length is approximately 200 ft.
Step-by-step explanation:
To find the dimensions of the rectangular parcel of land, let's assume that the length of the land is L ft and the width is W ft.
The problem states that the area of the land is 5000 ft², so we can write the equation L * W = 5000.
The problem also states that the diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel. We can use the Pythagorean theorem to find a relationship between the length, width, and diagonal. According to the theorem, the square of the length plus the square of the width equals the square of the diagonal. So we have L² + W² = (L+10)².
Now we have a system of two equations. We can solve this system to find the dimensions of the land. Substituting the value of L from the first equation into the second equation, we get (5000/W)² + W² = (5000/W + 10)².
After simplifying and solving this equation, we find that the width of the land is approximately 25 ft and the length is approximately 200 ft.