The three sides of a triangle are n, 3n + 13𝑛+1, and 5 n − 85𝑛−8. If the perimeter of the triangle is 56cm56cm, what is the length of each side?Separate multiple entries with a comma.
Question
The three sides of a triangle are n, 3n + 13𝑛+1, and 5 n − 85𝑛−8. If the perimeter of the triangle is 56cm56cm, what is the length of each side?Separate multiple entries with a comma.
Solution
The perimeter of a triangle is the sum of the lengths of all its sides. According to the problem, the sides of the triangle are n, 3n + 1, and 5n - 8, and the perimeter is 56 cm.
So, we can set up the equation:
n + (3n + 1) + (5n - 8) = 56
Combine like terms:
9n - 7 = 56
Add 7 to both sides of the equation:
9n = 63
Divide both sides by 9:
n = 7
Now that we know n = 7, we can find the lengths of the sides:
First side: n = 7 cm
Second side: 3n + 1 = 3*7 + 1 = 22 cm
Third side: 5n - 8 = 5*7 - 8 = 27 cm
So, the lengths of the sides of the triangle are 7 cm, 22 cm, and 27 cm.
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