Answer:
50
Step-by-step explanation:
FIRST, we need variables. Once we define variables, it's much easier to turn this word problem into a math problem.
Let a = first side
Let b = second side
Let c = third side
NOW, we can turn the words into equations:
"a triangle has a perimeter of 165 cm."
a + b + c = 165
"the first side is 65cm less than twice the second side."
a = 2b - 65
"the third side is 10cm less than the second side."
c = b - 10
Before we finish, I have to ask: Who writes problems like this??? Pointless problems like these are why kids don't like math! Ugh. Drives me crazy. It's a shame, because solving math problems really does have a certain satisfaction, once you learn how. [Okay. I'm done. Back to the problem.]
If we could get this to have only one variable, we could solve it. Substitution to the rescue!
a + b + c = 165 (rewrote equation from above)
(2b - 65) + b + (b - 10) = 165 (substituted "a" and "c" from equations above)
See how that works? Let's solve it.
2b - 65 + b + b - 10 = 165 (dropped the parentheses, because there was nothing to distribute, not even a minus sign)
4b - 75 = 165 (combined like terms)
4b = 240 (added 75 to both sides)
b = 60 (divided both sides by 4)
We found the second side! We can find the first and third sides using those equations from above:
a = 2b - 65
a = 2*60 - 65
a = 120 - 65
a = 55
c = b - 10
c = 60 - 10
c = 50
All done.
