SOLUTION: Please help me solve this problem: A city park in the shape of a right triangle has an area of 450√3 square yards. One leg of the triangle measures half the length of the hy

Algebra ->  Triangles -> SOLUTION: Please help me solve this problem: A city park in the shape of a right triangle has an area of 450√3 square yards. One leg of the triangle measures half the length of the hy      Log On


   

Question 1045756: Please help me solve this problem: A city park in the shape of a right triangle has an area of 450√3 square yards. One leg of the triangle measures half the length of the hypotenuse. What are the dimensions of the park?
Answer by josgarithmetic(39795) About Me  (Show Source):
You can put this solution on YOUR website!
h for hypotenuse
y for height
x for length

AREA:
%281%2F2%29xy=450sqrt%283%29

Either leg,
x=h%2F2

The triangle is a RIGHT Triangle.
x%5E2%2By%5E2=h%5E2


System of Equations:
system%28%281%2F2%29xy=450sqrt%283%29%2Ch=2x%2Cx%5E2%2By%5E2=h%5E2%29, having one modification done already.

Another modification,
system%28xy=900sqrt%283%29%2Ch=2x%2Cx%5E2%2By%5E2=h%5E2%29
Take the rest of the process; a few or several algebra steps. The obvious first step is substitute for h in the Pythagorean Theorem relationship equation.