SOLUTION: A gardener wants to divide a square piece of lawn in half diagonally. What is the length of the diagonal if the side of the square is 8 ft? Leave your answer in simplest radical fo

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A gardener wants to divide a square piece of lawn in half diagonally. What is the length of the diagonal if the side of the square is 8 ft? Leave your answer in simplest radical fo      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 708697: A gardener wants to divide a square piece of lawn in half diagonally. What is the length of the diagonal if the side of the square is 8 ft? Leave your answer in simplest radical form.
(1 point)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Each half would be a right isosceles triangle with both legs measuring 8 ft.
The diagonal would be the hypotenuse shared by those triangles.
We need to find the length, d, in feet, of that hypotenuse.

The Pythagorean theorem says that
the squares of the legs' lengths add up to
the squares of the length of the hypotenuse, so
8%5E2%2B8%5E2=d%5E2 --> d%5E2=2%2A8%5E2 --> d=sqrt%282%2A8%5E2%29 --> d=sqrt%282%29%2Asqrt%288%5E2%29%29 --> highlight%28d=8sqrt%282%29%29