Geometry Math Problem?

Question

INstead of walking along two sidesof a rectangluar field, Fran took a shortcut along the diagonal, thus saving distance equal to half the length of the longer side. Find hte length of the long side of the field, given that the length of the short side is 156 meters.

Answer 1

You have a right triangle with sides L (the long side), S (the short side), and D (the diagonal). You know that:

"The length of the short side is 156 meters."

S = 156

"Instead of walking along two sidesof a rectangular field, Fran took a shortcut along the diagonal, thus saving distance equal to half the length of the longer side."

L + S = D + 1/2 L

And the Pythagorean Theorem gives you

L² + S² = D²

You now have three equations in three unknowns (well, two, since you're given S); solve for the two remaining sides of the triangle.

Answer 2

Let's name x the long side.Then
the diagonal d=156+x-x/2
d=156+x/2
From Pythagorean Theorem
(156+x/2)^2=156^2+x^2
3x^2-624x=0
x nonzero,so
3x=624
x=208