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Question 1
Consider the triangle below.

(The image appears to depict geometric shapes, specifically a triangle and a line. The triangles are likely represented by the equation "5x-2," which is repeated three times. This suggests a focus on various configurations or representations of this specific shape in relation to the mathematical expression provided.)

(2 points)
Length of each side of the triangle =
units.

The perimeter of the triangle is
units. Remember to simplify the expression.

1 answer

To solve the problem, we first need to understand the details provided regarding the triangle and the equation. It looks like the equation "5x - 2" represents the lengths of the sides of the triangle. Assuming that the triangle is an equilateral triangle with all sides equal to \(5x - 2\), we can find the lengths of the sides and the perimeter.

  1. Length of each side: Given that each side of the triangle is \(5x - 2\), we just need to express that:

    \[ \text{Length of each side} = 5x - 2 \text{ units.} \]

  2. Perimeter of the triangle: The perimeter \(P\) of a triangle with three equal sides is calculated as:

    \[ P = \text{side length} + \text{side length} + \text{side length} = 3 \times \text{side length}. \]

    Plugging in the length of each side, we get:

    \[ P = 3(5x - 2). \]

    Now, we distribute the 3:

    \[ P = 15x - 6 \text{ units.} \]

So, the answers to your questions are:

  • Length of each side of the triangle = \(5x - 2\) units.
  • The perimeter of the triangle = \(15x - 6\) units (simplified).

Make sure to replace \(x\) with a specific numerical value if that is required for a specific situation or the problem context.