SOLUTION: triangle yzx given has 3 congruent angles 60 degrees top leg = 8. another leg = 3x-y, last leg is x + 3y + 2. find x and y. This is section 4.4 masters level b p.71 using triangle

Question 227055: triangle yzx given has 3 congruent angles 60 degrees top leg = 8. another leg = 3x-y, last leg is x + 3y + 2. find x and y. This is section 4.4 masters level b p.71 using triangle congruence holt 2004 problem 5. I have the answer which is x = 3 y = 1 but have no idea how they get there and I have to teach my son. Thanks for any help in understanding its been 30 something years.
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
the triangle has three equal angles, so it also has three equal sides

8 = 3x + y = x + 3y + 2

3x + y = 8 ___ y = 8 - 3x

x + 3y + 2 = 8 ___ x + 3y = 6

substituting ___ x + 3(8 - 3x) = 6 ___ x + 24 - 9x = 6

24 - 8x = 6 ___ 18 = 8x ___ 9/4 = x

substituting ___ y = 8 - 3(9/4) = 5/4
RELATED QUESTIONS
I am trying to find a leg length of a right 30-60-90 triangle. The shortest leg is y,... (answered by Alan3354)

given the right triangle A with hypotenuse length of x+3 and a leg length x. and the... (answered by Edwin McCravy)

in30 60 90 triangle and one leg is 8.5 and i need to find x and y ? (answered by stanbon)

In a 30 60 90 triangle the shorter leg is 8.5 i need to find x and y (answered by stanbon)

you have a right triangle with one angle at 55degrees and one leg 8m the longest leg is y (answered by Fombitz)

doing special right triangles (30-60-90) - if you are given a 30-60-90 triangle and the... (answered by josmiceli)

Fundamental Ideas Points, Lines, and Planes Postulates and Theorems Segments,... (answered by richard1234)

HI! so this is the question i've been meaning to ask: 1. One leg of a right triangle... (answered by swincher4391)

If the base and a leg of one isosceles triangle are congruent to the base and a leg of... (answered by ikleyn)