the perimeter of a triangle is 76 centimeters. the second side is twice as long as the first side. the third side is four centimeters shorter than the second side. how long is each side?
To find the lengths of the sides of the triangle, let's assign variables to represent the lengths:
Let's say the first side of the triangle = x centimeters
Since the second side is twice as long as the first side, the second side = 2x centimeters
And since the third side is four centimeters shorter than the second side, the third side = 2x - 4 centimeters
Now, the perimeter of a triangle is the sum of the lengths of its sides.
Given that the perimeter of the triangle is 76 centimeters, we can set up the equation:
x + 2x + (2x - 4) = 76
Let's solve for x:
5x - 4 = 76
5x = 80
x = 16
Now we can find the lengths of all three sides of the triangle:
First side = x = 16 centimeters
Second side = 2x = 2 * 16 = 32 centimeters
Third side = 2x - 4 = 2 * 16 - 4 = 28 centimeters
Therefore, the lengths of the sides of the triangle are:
First side = 16 centimeters
Second side = 32 centimeters
Third side = 28 centimeters
Let x = first side,
then 2x = second side and
2x - 4 = third side.
x + 2x + 2x - 4 = 76
Solve for x.