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Use the image to answer the question.

An illustration shows the unfolded version of a prism comprising of 2 triangles and 3 rectangles. Dimensions are marked. There are three adjoining rectangles positioned horizontally. The first and third rectangles appear identical. The second rectangle in the middle is smaller and is labeled as 3 inches in length and 2 inches in width. The center rectangle shares its top and bottom sides with the bases of identical triangles. A side of the bottom triangle is labeled 6 inches. The top side of the third rectangle on the right is marked as a line connecting point upper A on the upper right vertex and point upper B on the upper left vertex. All the common sides are shown as dashed lines.

What is the length of AB
?(1 point)
in.

1 answer

To find the length of \( AB \), we will use the dimensions provided in the illustration of the prism.

From the information given:

  • The middle rectangle has a length of 3 inches and a width of 2 inches.
  • The rectangles are positioned horizontally and appear to have the triangles at the ends.

Since the triangles are identical and the bottom side of the left triangle is at the bottom of the first rectangle, we will consider the following:

The two triangles are positioned such that their bases align with the tops of the rectangles. Since the height of the middle rectangle is 2 inches, it sets the vertical space that the triangles occupy.

We know that the bottom edge of the triangle that shares with point A and point B (the upper vertices) must be equal to the distance across the width of the rectangles.

Without specific angles or other height information about the triangles, we can reasonably assume the triangles' heights reach up from the top edge of the middle rectangle. As the bottom side of the left triangle is referenced, this means we can infer that the total vertical height provided by the triangles is also affected by any vertical distance from the top of the middle rectangle to the peak of the triangles.

Given that the triangles are also are implied to be merely extending upward from each rectangle, this can lead us to understand that \(AB\) lies across the entire width of the prism structure.

Solution:

Assuming that the two triangles are positioned such that they are aligned perfectly on the horizontal base:

  • First Rectangle Width: 3 inches
  • Second Rectangle Width: 3 inches
  • Third Rectangle Width: 3 inches

So, the total width across points A and B is calculated as: \[ AB = \text{width of left rectangle} + \text{width of middle rectangle} + \text{width of right rectangle} = 3 + 3 = 6 \text{ inches} \]

Thus, the length of \(AB\) is: \[ \boxed{6} \text{ in} \]