Question

The three sides of a triangle are n, 3n+3, and 2n+11. If the perimeter of the triangle is 50 inches, what is the length of each side?

Answer 1

6, 21, and 23 inches

Explanation:

The perimeter of a triangle is equal to the sum of all side lengths in that triangle. We're given the perimeter as 50 inches, and the side lengths as n, 3n + 3, and 2n + 11.

• This means that we can algebraically solve the equation
  `n + 3n + 3 + 2n + 11 = 50`

Step 1: Combine like terms.

• 
  `(n+3n+2n) + (3+11) = 50`
• 
  `6n + 14 = 50`

Step 2: Subtract 14 from both sides.

• 
  `6n + 14 - 14 = 50 - 14`
• 
  `6n = 36`

Step 3: Divide both sides by 6.

• 
  `6n/6 = 36/6`
• 
  `n = 6`

Step 4: Plug in the value of n as 6 in each side.

• 
  `(6) + (3(6) + 3) + (2(6)+11) = 50`
• 
  `(6) + (18+3) + (12+11) = 50`
• 
  `(6) + (21) + (23) = 50`

Therefore, the side lengths are 6, 21, and 23 inches.

Have a lovely rest of your day/night, and good luck with your assignments! ♡