Question

Can someone please help me with this? I keep getting half of the answer and I'm doing everything right. ------------------------- The perimeter of any triangle is the sum of the lengths its sides. The lengths of the sides of a certain triangle, in feet, are consecutive even integers. The perimeter of this triangle is between 10 feet and 24 feet inclusive. a. Using one variable, write three expressions that represent the lengths of the three sides of the triangle. b. Write a compound inequality to model this problem. c. Solve the inequality. List all possible lengths for the longest side of the triangle. ------------------------- This is what I have so far... (please tell me what I did wrong as well) ------------------------- 10 ≤ x+(x+2)+(x+4) ≤ 24 ------------------------- 10 ≤ 3x+6 ≤ 24 -------------------------4 ≤ 3x ≤ 18 ------------------------- 4/3 ≤ x ≤ 6

Answer 1

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Answer:

  a. x, x+2, x+4

  b. 10 ≤ 3x+6 ≤ 24

  c. 6 ft, 8 ft, or 10 ft

Step-by-step explanation:

Given:

• The lengths of the sides of a certain triangle, in feet, are consecutive even integers.
• The perimeter of this triangle is between 10 feet and 24 feet inclusive.

Find:

  a. Using one variable, write three expressions that represent the lengths of the three sides of the triangle.

  b. Write a compound inequality to model this problem.

  c. Solve the inequality. List all possible lengths for the longest side of the triangle.

Solution:

You have let x represent the shortest side. (Note that the question asks for the length of the longest side.)

a. The expressions for side lengths can be x, x+2, x+4 when x is the shortest side.

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b. Here is the compound inequality

  10 ≤ x+(x+2)+(x+4) ≤ 24

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c. Here is the solution

  10 ≤ 3x+6 ≤ 24 . . . . collect terms

  4 ≤ 3x ≤ 18 . . . . . . . subtract 6

  4/3 ≤ x ≤ 6 . . . . . . . . divide by 3

Your working is correct, but incomplete. The values of interest are the even integers x+4.

  5 1/3 ≤ x+4 ≤ 10

The longest side may be 6 ft, 8 ft, or 10 ft.