Questions: A flower bed is in the shape of a triangle with one side twice the length of the shortest side and the feet more than the length of the shortest side. Find the dimensions if the perimeter is 133 feet. What is the length of the shortest side? The length of the shortest side is 26 feet. What is the length of the second side?

Solution Steps

To solve this problem, we need to set up an equation based on the given information about the sides of the triangle and its perimeter. Let's denote the shortest side as \( x \). According to the problem, the second side is twice the length of the shortest side, so it is \( 2x \). The third side is 7 feet more than the length of the shortest side, so it is \( x + 7 \). The perimeter of the triangle is the sum of all its sides, which is given as 133 feet. We can set up the equation \( x + 2x + (x + 7) = 133 \) and solve for \( x \).

1. Define the shortest side as \( x \).
2. Express the second side as \( 2x \).
3. Express the third side as \( x + 7 \).
4. Set up the equation for the perimeter: \( x + 2x + (x + 7) = 133 \).
5. Solve for \( x \).

Let the shortest side of the triangle be \( x \). According to the problem, the second side is twice the length of the shortest side, so it is \( 2x \). The third side is 7 feet more than the length of the shortest side, so it is \( x + 7 \).

The perimeter of the triangle is the sum of all its sides, which is given as 133 feet. Therefore, we can set up the equation: \[ x + 2x + (x + 7) = 133 \]

Combine like terms: \[ 4x + 7 = 133 \]

Subtract 7 from both sides: \[ 4x = 126 \]

Divide by 4: \[ x = \frac{126}{4} = \frac{63}{2} \]

• The shortest side is \( x = \frac{63}{2} \) feet.
• The second side is \( 2x = 2 \times \frac{63}{2} = 63 \) feet.
• The third side is \( x + 7 = \frac{63}{2} + 7 = \frac{63}{2} + \frac{14}{2} = \frac{77}{2} \) feet.

Final Answer