SOLUTION: The diagonal of a square is 2 meters longer than a side. Find the length of a side.

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: The diagonal of a square is 2 meters longer than a side. Find the length of a side.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 201933: The diagonal of a square is 2 meters longer than a side. Find the length of a side.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let s = the length of the side of the square, then the length of the diagonal is:
s%2B2%29.
Using the Pythagorean relationship for the sides of a right triangle (c%5E2+=+a%5E2%2Bb%5E2) in which c is the diagonal of the square, so:c+=+s%2B2 and...
%28s%2B2%29%5E2+=+s%5E2%2Bs%5E2 Expand the left side.
s%5E2%2B4s%2B4+=+2%2As%5E2 Subtract 2%2As%5E2 from both sides.
-s%5E2%2B4s%2B4+=+0 Use the quadratic formula to solve: s+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a where: a = -1, b = 4, and c = 4
s+=+%28-4%2B-sqrt%284%5E2-4%28-1%29%284%29%29%29%2F2%28-1%29
s+=+%28-4%2B-sqrt%2816-%28-16%29%29%29%2F%28-2%29
s+=+%28-4%2B-sqrt%2832%29%29%2F%28-2%29
highlight%28s+=+2%2B2sqrt%282%29%29 or highlight_green%28s+=+2-2sqrt%282%29%29 Discard the negative (green) solution as the length of the side of a square is a positive value (red).
+s+=+2%2B2sqrt%282%29 This is the exact value of the side of the square.
+s+=+4.828 This is the approximate value.