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.
