Question 868: A triangle has a perimeter of 197 cm. The sum of the smallest and medium sides is 49 more than the longest side. The difference between the longest and shortest sides is 22. Find the legth of all three sides.
HELP!
I know I have to solve by coming p with a system of equation, what I have is:
X=longest, Y=shortest, Z=medium
Y + Z = X + 49
X - 22 = Y
X + Y + Z = 197
Thank you for your time.
Answer by usyim88hk(158)   (Show Source):
You can put this solution on YOUR website! x = y+z-49
x = y+22
therefore y+22 = y+z-49 because x = y+z-49 = y+22
y+22 = y+z-49
y+22-y-22 = y+z-49-y-22
0 = z-71
0+71 = z-71+71
[z = 71] ( So now we know that z is 71 )
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x+y+z = 197 ( z = 71 )
x+y+71 = 197
x+y = 126
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x-y = 22 ( x-22=y so x-y=22 )
x+y = 126 ( use subtitution to slove for x )
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2x = 148
[x = 74]
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x+y+z = 197
74+y+71 = 197
[y = 52]
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So [x = 74] (the longest side)
[y = 52] (the shortest side)
[z = 71] (the medium side)
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