A triangle has a perimeter of 32 inches. The medium side is 7 more than the short side, and the longest side is3 times the length of the shortest side. Find the shortest side.

x + (x + 7) + 3x = 32

5x + 7 = 32

5x = 25

x = ?

Let's denote the shortest side as x.

According to the given information, the medium side is 7 more than the short side, so its length is x + 7.

The longest side is 3 times the length of the shortest side, so its length is 3x.

The perimeter of a triangle is the sum of the lengths of its sides. Therefore, we can set up the equation:

x + (x + 7) + 3x = 32

Combining like terms:

5x + 7 = 32

Subtracting 7 from both sides:

5x = 25

Dividing both sides by 5:

x = 5

Therefore, the shortest side of the triangle is 5 inches.

To find the shortest side of the triangle, let's use algebraic equations to represent the relationships between the sides.

Let's assume the length of the shortest side is x inches.

According to the given information:
- The medium side is 7 more than the short side, so its length is x + 7 inches.
- The longest side is 3 times the length of the shortest side, so its length is 3x inches.

The sum of the lengths of all three sides of a triangle is equal to its perimeter. Therefore, we can write the following equation:

x + (x + 7) + 3x = 32

Now, let's solve this equation to find the value of x, which represents the shortest side:

Combine like terms:
5x + 7 = 32

Subtract 7 from both sides:
5x = 32 - 7
5x = 25

Divide both sides by 5:
x = 25 / 5
x = 5

Hence, the shortest side of the triangle measures 5 inches.

A triangle has a perimeter of

32
inches. The medium side is
4
more than the short side, and the longest side is
5
times the length of the shortest side. Find the shortest side.