Respuesta :
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.
PLEASE MARK ME AS BRAINLIEST
Step One - Define the Unknown Variable
First we need to define our unknown variable. For this case, I am going to use the letter 's' for the second side of the triangle (no actually because the question told you to). The reason I am using the second side as the unknown is because the second side is independent. The first and third sides' lengths depend on the length of the second side.
Step Two - Write an Equation
We need to use what we know to write the equation. First, we know that the perimeter of a polygon is the sum of the lengths of all the sides. The first side is 65 less than two times 's'. This would be 2s-65. The second side is just s. The third side is 10 less than 's'. So it would be s-10. The perimeter is all of the sides added up, so the expression for all the sides added up is (2s-65)+(s)+(s-10). The first, second, and third side added up is 165. So the equation for 1. is (2s-65)+(s)+(s-10) = 165.
Step Three - Solve the Equation
To solve the equation, you need to isolate the variable, which is 's'.
First, let's simplify the equation.
(2s-65)+(s)+(s-10) = 165.
4s-75 = 165.
Now we need to remove the 75. To get rid of the 75, you must add 75. But since you are adding 75 to one side of the equation, you must add 75 to the other side of the equation to make it equal.
4s-75+75 = 165+75
4s = 240
Now we need to remove the 4. To get rid of the 4, you have to divide each side by 4.
4s÷4 = 240÷4
s = 60
The length of the second side is 60 cm.
Step Four - Find the Lengths of all Sides
Now we know the length of the second side, we can find the length of the other sides.
The first side is 65 less than two times of 60.
Two times of 60 is 60×2 or 120.
65 less than 120 is 120-65 or 55.
The first side is 55 cm.
The third side is 10 less than 60.
10 less than 60 is 60-10 or 50.
The third side is 50.
So the lengths of the three sides are 55, 60, and 50.
Step Five - Check Your Answer
Now let's see if the three sides added up equals to 165.
Well, 55+60+50 does equal 165, so we know this is right.
The equation that represents the perimeter of the triangle is (2s + 65) + (s) + (s + 10) = 165. The length of each side of the triangle is 55, 60, and 50.
