A rectangular parcel of land is 210 ft wide. The length of a diagonal between opposite corners is 70 ft more than the length of the parcel. What is the length of the parcel?

Width of the rectangular parcel of land = 210 ft.

Let us assume length of the parcel = x ft.

We are given "the length of a diagonal between opposite corners is 70 ft more than the length of the parcel."

We took x feet for the length of the parcel.

70 ft more than x would be = (x+70).

Diagonal, length and width of the parcel form a right angle triangle, because all angles of a rectangle of 90 degree.

Therefore, we would apply Pythagorean Theorem in that right triangle to find the value of x.

(Width) ^2 + (Lengh) ^2 = (Diagonal) ^2

Plugging values of width, length and diagonal in the above formula.

(210) ^2 + (x) ^2 = (x+70) ^2

44100 + x^2 = x^2 + 4900 + 140x.

Subtracting both sides 4900, we get

44100 + x^2-4900 = x^2 + 4900 + 140x-4900.

39200 + x^2 = x^2 + 140x

Subtracting x^2 from both sides.

39200 + x^2-x^2 = x^2 + 140x-x^2

39200 = 140x

Dividing both sides by 140, we get

39200/140 = 140x/140

x=280 ft.

Therefore, length of the parcel is 280 ft.