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rosijanka [135]
3 years ago
5

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
Mathematics
1 answer:
serg [7]3 years ago
6 0

9514 1404 393

Answer:

  a. x, x+2, x+4

  b. 10 ≤ 3x+6 ≤ 24

  c. 6 ft, 8 ft, or 10 ft

Step-by-step explanation:

<u>Given</u>:

  • 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.

<u>Find</u>:

  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.

<u>Solution</u>:

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.

__

b. Here is the compound inequality

  10 ≤ x+(x+2)+(x+4) ≤ 24

__

c. Here is the solution

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

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

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

<em>Your working is correct, but incomplete</em>. 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.

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The total length of a boundary defines the perimeter of an equilateral triangle.

<h3>What is the Perimeter of an Equilateral Triangle?</h3>
  • The total of the three sides makes up the perimeter of an equilateral triangle.
  • The following fundamental characteristics define a triangle as being equilateral:
  1. The three sides are equal.
  2. There is a 60° angle between all three.
  • The sides of the triangle PQ = QR = RP in the following illustration have equal lengths.
  • The triangle's angles are also equal in addition to this. An equilateral triangle is what this is.
  • An equilateral triangle's perimeter is now equal to 3a, where a denotes one of the triangle's sides.
  • Perimeter of Equilateral Triangle Formula : P = 3a, where 'a' stands for one of the triangle's sides, is a simple formula for calculating an equilateral triangle's perimeter. An equilateral triangle has three equal sides, hence the sum is equal to three equal sides, or 3a.
  • Additional equilateral triangle formulas include the following: When we need to determine a triangle's height from its sides, we can apply the following formula: Equilateral Triangle Height = (3a)/2
  • The semi-perimeter of an equilateral triangle must be determined in a few situations. Half of a perimeter, or semi-perimeter, is equal to 3a/2, which is derived using the formula semi-perimeter = (a + a + a)/2.

To Learn more About equilateral triangle refer to:

brainly.com/question/15294703

#SPJ4

3 0
1 year ago
Read 2 more answers
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