SOLUTION: in the figure triangle abc is an equilateral triangle such that ab=(y+8)cm ac=(x+10)cm and bc= 2(x+y)cm. solve x and y

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Question 930767: in the figure triangle abc is an equilateral triangle such that ab=(y+8)cm ac=(x+10)cm and bc= 2(x+y)cm.
solve x and y
Found 3 solutions by Shin123, greenestamps, MathTherapy:
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
All 3 sides are the same as mentioned. y%2B8=x%2B10=2x%2B2y
y%2B8=x%2B10
y=x%2B2
2x%2B2%28x%2B2%29
2x%2B2x%2B4
4x%2B4
x%2B10=4x%2B4
x=4x-6 Please repost.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The three side lengths are the same: y+8, x+10, and 2(x+y).

Use the first two expressions to get one variable in terms of the other; then substitute in the third expression and compare it to the second:

y%2B8=x%2B10
y+=+x%2B2
x%2B10+=+2%28x%2B%28x%2B2%29%29
x%2B10+=+4x%2B4
6+=+3x
x+=+2

x=2; y = x+2 = 4

The three side lengths are
y+8 = 4+8 = 12
x+10 = 2+10 = 12
2(x+y) = 2(6) = 12

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
in the figure triangle abc is an equilateral triangle such that ab=(y+8)cm ac=(x+10)cm and bc= 2(x+y)cm.
solve x and y 
Side AB = AC, and so: y + 8 = x + 10____x - y = - 2 ------ eq (i)

Side BC = AC, and so: 2(x + y) = x + 10___2x + 2y = x + 10____2x - x + 2y = 10____x + 2y = 10 ------- eq (ii)

3y = 12 ------ Subtracting eq (i) from eq (ii)

highlight_green%28matrix%281%2C5%2C+y%2C+%22=%22%2C+12%2F3%2C+%22=%22%2C+4%29%29

x - 4 = - 2 ------- Substituting 4 for y in eq (i) 

x = - 2 + 4

highlight_green%28matrix%281%2C3%2C+x%2C+%22=%22%2C+2%29%29

OR

You could choose any other combinations of 2 sides, and solve for the 2 variables.