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Represent the perimeter of each triangle with an expression in simplest form. Which triangle has a greater perimeter if x = 4? Will this be true for any positive value of x? Justify your response



Answer :

Using the perimeter concept, we have that:

  • For triangle 1, the perimeter is given by: P1(x) = 7x + 69.
  • For triangle 2, the perimeter is given by: P2(x) = 13x + 47.
  • With x = 4, triangle 2 has a greater perimeter.
  • This is not true for any positive number x, as for x < 3.67, the perimeter of triangle 1 is greater than the perimeter of triangle 2.

What is the missing information?

The triangles are missing, and they are given by the image at the end of the answer.

What is the perimeter of a polygon?

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure.

Hence, for each triangle, the perimeters are given as follows:

  • P1(x) = 6x + 7x + 3(-2x + 23) = 7x + 69.
  • P2(x) = 5x + 2 + 8x + 45 = 13x + 47.

When x = 4, the perimeters are given as follows:

  • P1(4) = 7(4) + 69 = 97.
  • P2(4) = 13(4) + 47 = 99.

With x = 4, triangle 2 has a greater perimeter.

To find when each perimeter is greater, we solve the following inequality:

P1(x) > P2(x)

7x + 69 > 13x + 47

-6x > -22

6x < 22

x < 3.67.

Hence, this is not true for any positive number x, as for x < 3.67, the perimeter of triangle 1 is greater than the perimeter of triangle 2.

More can be learned about the perimeter of a polygon at https://brainly.com/question/3310006

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View image joaobezerra

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