SOLUTION: The hypotenuse of a right triangle is 2.4 units long. The longer leg is 1.7 units longer than the shorter leg. Find the lengths of the sides of the triangle.

Algebra ->  Triangles -> SOLUTION: The hypotenuse of a right triangle is 2.4 units long. The longer leg is 1.7 units longer than the shorter leg. Find the lengths of the sides of the triangle.       Log On


   

Question 141336: The hypotenuse of a right triangle is 2.4 units long. The longer leg is 1.7 units longer than the shorter leg. Find the lengths of the sides of the triangle.
Answer by nabla(475) About Me  (Show Source):
You can put this solution on YOUR website!
hyp=2.4
let l=longer leg, s= shorter leg
l=1.7+s
From the Pythagorean Theorem, a^2+b^2=c^2, c=hypotenuse.
s%5E2%2B%281.7%2Bs%29%5E2=2.4%5E2
s%5E2%2B1.7%5E2%2B3.4s%2Bs%5E2=2.4%5E2
2s%5E2%2B3.4s%2B2.89=5.76
2s%5E2%2B3.4s-2.87=0
Normally we would continue here by applying the quadratic formula, however I see a factorization to make it easier:
2%28-.618843%2Bs%29%280.231884%2Bs%29=0
The only answer that makes sense (that is, it is positive), is s=.618843.
So, l=1.7+s=1.7+.618843=2.31884.
Now, check:
.618843%5E2%2B%28.618843%2B1.7%29%5E2=.382967%2B5.37703=5.76
and 2.4%5E2=5.76. This completes the problem.