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.