Question

the ratio of the measures of the sides of a triangle is 9:12:5. if the perimeter of the triangle is 130 feet, find the measures of the sides.
3.
shortest side =
middle side =
longest side =

Explanation:

Step1: Define variables for sides

Let the sides of the triangle be \(9x\), \(12x\), and \(5x\) (where \(x\) is a positive real number).

Step2: Use perimeter formula

The perimeter of a triangle is the sum of its sides. So, \(9x + 12x + 5x=130\).
Combine like terms: \(26x = 130\).

Step3: Solve for \(x\)

Divide both sides by 26: \(x=\frac{130}{26}=5\).

Step4: Find each side

• Shortest side (\(5x\)): \(5\times5 = 25\) feet.
• Middle side (\(9x\)): \(9\times5 = 45\) feet.
• Longest side (\(12x\)): \(12\times5 = 60\) feet.

Answer:

Shortest side = 25 feet
Middle side = 45 feet
Longest side = 60 feet