Answered

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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?

Sagot :

renknee

Answer:

6, 21, and 23 inches

Step-by-step 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 [tex]n + 3n + 3 + 2n + 11 = 50[/tex]

Step 1: Combine like terms.

  • [tex](n+3n+2n) + (3+11) = 50[/tex]
  • [tex]6n + 14 = 50[/tex]

Step 2: Subtract 14 from both sides.

  • [tex]6n + 14 - 14 = 50 - 14[/tex]
  • [tex]6n = 36[/tex]

Step 3: Divide both sides by 6.

  • [tex]6n/6 = 36/6[/tex]
  • [tex]n = 6[/tex]

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

  • [tex](6) + (3(6) + 3) + (2(6)+11) = 50[/tex]
  • [tex](6) + (18+3) + (12+11) = 50[/tex]
  • [tex](6) + (21) + (23) = 50[/tex]  

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

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