One side of triangle is one-third the longest side. The third side is 13 feet less than the longest side. The perimeter is 106. Find all three sides.
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To solve this problem, we'll need to set up equations based on the information provided. Let's denote the longest side as "x."
According to the given information:
- One side of the triangle is one-third the longest side: Therefore, the length of this side can be represented as (1/3)x.
- The third side is 13 feet less than the longest side: Therefore, the length of this side can be represented as x - 13.
We also know that the perimeter of a triangle is the sum of all three sides. In this case, the perimeter is given as 106. So, we can set up the equation:
(1/3)x + x + (x - 13) = 106
Now, we can solve this equation to find the value of x, which will represent the longest side. Then, we can substitute this value back into our equations to find the lengths of the other two sides.
Let's solve the equation step by step:
First, combine like terms:
(1/3)x + x + x - 13 = 106
(7/3)x - 13 = 106
Next, simplify by multiplying both sides by 3:
7x - 39 = 318
Then, isolate the variable x by adding 39 to both sides:
7x = 357
Finally, divide both sides by 7 to solve for x:
x = 51
Now that we know the value of x, we can substitute it back into our equations to find the lengths of the other two sides:
One side of the triangle = (1/3)x = (1/3) * 51 = 17 feet
The third side of the triangle = x - 13 = 51 - 13 = 38 feet
So, the lengths of the three sides are:
Longest side = 51 feet
One side = 17 feet
Third side = 38 feet
Put all the sides in terms of x. X represents the longest side
side x
side y=(1/3)x
side z=x-13
The perimeter is 106 which is the sum of all the sides.
x+(1/3)x+(x-13)=106
Solve for x
Then it will be easy to find the other sides