SOLUTION: In right triangle ABC where angle A is 90 degrees, AC = 3x and BC = 5x. if the perimeter of triangle ABC is 84, then what is x?

Algebra ->  Triangles -> SOLUTION: In right triangle ABC where angle A is 90 degrees, AC = 3x and BC = 5x. if the perimeter of triangle ABC is 84, then what is x?      Log On


   

Question 252398: In right triangle ABC where angle A is 90 degrees, AC = 3x and BC = 5x. if the perimeter of triangle ABC is 84, then what is x?
Found 2 solutions by edjones, drk:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
b=3x, c=5x
a^2+b^2=c^2
a^2+9x^2=25^2
a^2=16x^2
a=4x
3x+4x+5x=84
12x=84
x=7
.
Ed

Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
We have a right triangle with three sides: AC, BC, and AC. We know that AC = 3X, BC = 5X. If you drew this out, you would see that we are missing side AB. Let this side = KX, where K and X >= 1.
We apply the pythagorean theorem:
%283x%29%5E2+%2B+%28kx%29%5E2+=+%285x%29%5E2
this gives us
9x%5E2+%2B+k%5E2x%5E2+%2B+25x%5E2
divide out the X^2.
9+%2B+K%5E2+=+25
solve for K.
K^2 = 16
K = 4.
So, we are dealing with a 3x, 4x, 5x triangle. We need find to x knowing the perimeter = 84. We have
3x + 4x + 5X = 84
12x = 84
x = 7.