Question 845243: A triangle has a perimeter of 48 feet. The second side is 5 feet longer than the first. The third side is 3 feet longer than the first. What is the length of each side?
Answer by pmesler(52)   (Show Source):
You can put this solution on YOUR website! Let's start off with the formula for the perimeter of a triangle.
P = a + b + c, where a, b, and c are the lengths for the sides of the triangle.
Since we already given the perimeter in the problem, let's go ahead and substitute that into the equation.
48 = a + b + c.
Now, we are told that the second side is 5 feet longer than the first. The third side is 3 feet longer than the first.
Let a= the first side. Then let b = second side = a+5. Then let c = the third side = a+3
Now given these values, let's write out the equation again.
48 = a + (a + 5) + (a + 3).
Now we simply solve for a. Once we find a, we will be able to find b and c.
48 = a + (a + 5) + (a + 3).
Combine like terms to simplify.
48 = 3a + 8
Subtract 8 from both sides to isolate a.
40 = 3a
Divide both sides by 3.
a = 13.33
Now, to find the other sides. We know that a = 13.33,
that means b = 13.33 + 5 = 18.33 and c = 13.33 + 3 = 16.33
Now let's add up all the values to see if they equal 48.
13.33 + 18.33 + 16.33 = 47.99. When we round up it equals 48.
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