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?

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) (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) (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:

this gives us

divide out the X^2.

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.
RELATED QUESTIONS
In the right triangle ABC, AC= 12, angle B= 30 degrees, Angle C= 90 degrees, and Angle A= (answered by Alan3354)
in right triangle ABC, AB=20, AC=12, BC=16 and angle c is 90 degrees. find to the nearest (answered by Alan3354)
if a triangle ABC exists then what is the length of AB if AC=10 BC=6 and the angle ACB=... (answered by stanbon)
Given triangle ABC, where angle ABC is a right angle, AB =x,BC=y, and AC= (x + 4)2 , what (answered by ankor@dixie-net.com)
Given triangle ABC, where angle ABC is a right angle, AB=x, BC=y, and AC=(x + 4)^2, what... (answered by josgarithmetic)
if in triangle ABC, the measure of angle B is greater than 90 degrees, and AB= BC, what... (answered by MathLover1)
I need help with the following proof and CANNOT use any givens like all the angles of... (answered by richard1234)
In triangle ABC, linr CD is both the median and the altitude to side AB. If AB=5x+3,... (answered by ankor@dixie-net.com)
__ in triangle ABC, CD is both the median and the altitude if AB=... (answered by jsmallt9)