SOLUTION: A rectangular parcel of land is 50 ft. wide. The length of a diagonal between opposite corners is 10 ft more than the length of the parcel. What is the length of the parcel?

Algebra ->  Rectangles -> SOLUTION: A rectangular parcel of land is 50 ft. wide. The length of a diagonal between opposite corners is 10 ft more than the length of the parcel. What is the length of the parcel?      Log On


   

Question 776883: A rectangular parcel of land is 50 ft. wide. The length of a diagonal between opposite corners is 10 ft more than the length of the parcel. What is the length of the parcel?
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
Let the length be L ft and diagonal be D ft.

Using Pythagoras theorem
Diagonal%5E2+=+Length%5E2+%2B+Width%5E2
D%5E2+=+L%5E2+%2B+50%5E2 _______ (1)

Also, D+=+L+%2B+10

Substituting for D in terms of L in (1)
%28L+%2B+10%29%5E2+=+L%5E2+%2B+50%5E2
L%5E2+%2B+20L+%2B+100+=+L%5E2+%2B+2500
20L+=+2400
L+=+2400%2F20+=+120

The length is 120 ft.