the perimeter of a triangle is 49 centimeters. find the lenghts of its sides, if the longest side is 9 centimeters longer than the shorter side, and the remaining side is 4 centimeters longer than the shorter side.
i think it is ___________.
Let's denote the lengths of the sides of the triangle as x, x + 4, and x + 9.
The perimeter of a triangle is the sum of the lengths of its sides. So we have:
x + (x + 4) + (x + 9) = 49
Simplifying the equation:
3x + 13 = 49
Subtracting 13 from both sides:
3x = 36
Dividing both sides by 3:
x = 12
Therefore, the lengths of the sides of the triangle are:
Shortest side: x = 12 cm
Second side: x + 4 = 12 + 4 = 16 cm
Longest side: x + 9 = 12 + 9 = 21 cm
So the lengths of the sides are 12 cm, 16 cm, and 21 cm, respectively.
To find the lengths of the sides of the triangle, we can set up an equation based on the given information.
Let's assume that the shortest side of the triangle has a length of x centimeters.
According to the information given, the longest side is 9 centimeters longer than the shorter side. So, the length of the longest side is x + 9 centimeters.
Similarly, the remaining side is 4 centimeters longer than the shorter side. So, the length of the remaining side is x + 4 centimeters.
The perimeter of a triangle is the sum of the lengths of its sides. In this case, the perimeter is given as 49 centimeters. So, we can set up the equation:
x + (x + 9) + (x + 4) = 49
Now, let's solve this equation to find the value of x, which represents the length of the shortest side.
3x + 13 = 49
3x = 49 - 13
3x = 36
x = 36 / 3
x = 12
Therefore, the length of the shortest side is 12 centimeters.
Now, we can find the lengths of the other sides:
Longest side = x + 9 = 12 + 9 = 21 centimeters
Remaining side = x + 4 = 12 + 4 = 16 centimeters
So, the lengths of the sides of the triangle are 12 cm, 16 cm, and 21 cm.
49=x+(x+9)+(x+4)
49=3x+13
36=3x
12+x
so one side is 12cm, on is 16cm and one is 21cm