A triangle has a perimeter of 40cm40cm. If the three sides of the triangle are n, 3 n − 53𝑛−5, and3 n − 43𝑛−4, what is the length of each side?Separate multiple entries with a comma.
Question
A triangle has a perimeter of 40cm40cm. If the three sides of the triangle are n, 3 n − 53𝑛−5, and3 n − 43𝑛−4, 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. Given that the perimeter is 40 cm and the sides are n, 3n-5, and 3n-4, we can set up the following equation:
n + (3n - 5) + (3n - 4) = 40
Combine like terms:
7n - 9 = 40
Add 9 to both sides of the equation:
7n = 49
Divide both sides by 7:
n = 7
Substitute n = 7 into the expressions for the sides of the triangle:
First side: n = 7 cm Second side: 3n - 5 = 37 - 5 = 16 cm Third side: 3n - 4 = 37 - 4 = 17 cm
So, the lengths of the sides of the triangle are 7 cm, 16 cm, and 17 cm.
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