A triangle has a perimeter of 56 centimeters. Each of the two longer sides of the triangle is three times as long as the shortest side. Find the length of each side of the triangle
Let x = short side, then 3x = each other side.
x + 3x + 3x = 56
Solve for x, then 3x.
To solve this problem, let's first assign variables to represent the lengths of the sides of the triangle. We'll call the shortest side "x" centimeters.
According to the given information, the two longer sides are three times as long as the shortest side. So the lengths of the longer sides can be represented as "3x" and "3x" centimeters.
The perimeter of a triangle is the sum of the lengths of its sides. In this case, the perimeter is 56 centimeters.
So we can set up an equation to represent the perimeter:
x + 3x + 3x = 56
Now we need to solve this equation to find the value of "x".
Combining like terms on the left side of the equation, we get:
7x = 56
Dividing both sides of the equation by 7, we get:
x = 8
Now we know the length of the shortest side of the triangle, which is 8 centimeters.
To find the lengths of the longer sides, we can substitute the value of "x" back into our earlier expression.
The lengths of the longer sides are:
3x = 3 * 8 = 24 centimeters
Therefore, the length of each side of the triangle is:
Shortest side = 8 centimeters
Longer sides = 24 centimeters