The perimeter of a triangle is 45 centimeters. Find the lengths of its sides, if the longest side is 7 centimeters longer than the shortest side, and the remaining side is 2 centimeters longer than the shortest side.
Just translate into math:
shortest side --- x
longest side ---- x+7
remaining side --- x+2
solve:
x + x+7 + x+2 = 45
To solve this problem, let's represent the lengths of the sides of the triangle using variables.
Let's assume the shortest side is x centimeters long.
According to the problem, the longest side is 7 centimeters longer than the shortest side. Therefore, we can represent the length of the longest side as (x + 7) centimeters.
Similarly, the remaining side is 2 centimeters longer than the shortest side, so its length can be expressed as (x + 2) centimeters.
Now, let's find the perimeter of the triangle by adding up the lengths of all three sides:
Perimeter = x + (x + 7) + (x + 2)
Given that the perimeter is 45 centimeters, we can set up the following equation:
x + (x + 7) + (x + 2) = 45
Simplifying the equation, we have:
3x + 9 = 45
Now, let's solve for x:
3x = 45 - 9
3x = 36
x = 36 / 3
x = 12
So, the shortest side of the triangle is 12 centimeters long.
Now, we can calculate the lengths of the other two sides:
Longest side = x + 7 = 12 + 7 = 19 centimeters
Remaining side = x + 2 = 12 + 2 = 14 centimeters
Therefore, the lengths of the sides of the triangle are as follows:
Shortest side = 12 centimeters
Longest side = 19 centimeters
Remaining side = 14 centimeters