the perimeter of a triangle is 48 cm. The length of one side is 7 cm more than the length of the shortest side, and the length of the other side is 5 more than twice the shortest side. Find the shortest side.
x + 7 + 2x + 5 + x = 48
4x + 12 = 48
4x = 36
x = 36/4
x = 9
To solve this problem, we first need to understand the given information. Let's assign variables to represent the lengths of the sides of the triangle.
Let's say:
- x represents the length of the shortest side
- x + 7 represents the length of the second side (since it is 7 cm more than the shortest side)
- 2x + 5 represents the length of the third side (since it is 5 more than twice the shortest side)
The perimeter of a triangle is found by adding the lengths of all three sides together. In this case, we have:
Perimeter = x + (x + 7) + (2x + 5)
According to the given information, the perimeter of the triangle is 48 cm. So we can set up the equation:
48 = x + (x + 7) + (2x + 5)
Now we can solve for x:
48 = 4x + 12 (combine like terms)
48 - 12 = 4x
36 = 4x
x = 36/4
x = 9
So the shortest side of the triangle is 9 cm.