SOLUTION: This question is a mix between geometery and algebra. I have gotten past putting the values into a right angled triangle and then substituting it into the Pythagorean Theorem, but

Question 82817: This question is a mix between geometery and algebra. I have gotten past putting the values into a right angled triangle and then substituting it into the Pythagorean Theorem, but I don't know what to do next.

"A sail is in the shape of a right-angled triangle. The longest side of the sail is √3 times longer than the shortest side. The third side is 3m longer than the shortest side. Find the length of each sail."

Any help really appreciated.
Daniel
Answer by rapaljer(4551) (Show Source):
You can put this solution on YOUR website!
Let x = shortest side (a leg of the right triangle)
x+3 = longer side (a leg of the right triangle)
= longest side (hypotenuse of right triangle)

Set equal to zero, moving everything to the right side of the equation:

This does NOT factor (does this have an ugly answer??), so you'll have to complete the square or use the quadratic formula. I will complete the square:

Reject the negative answer, since a side of a triangle cannot be negative:
meters (shortest side)
meters (second leg of the right triangle)
meters (hypotenuse)
meters (hypotenuse)

R^2 at SCC