Question

Use the image to answer the question.

An illustration shows the unfolded version of a prism with rectangular base. Dimensions are labeled. Three adjoining rectangles are arranged horizontally. The second rectangle has an adjoining triangle on its top and another adjoining triangle on its bottom. The top and bottom of the rectangle form the bases of the triangles. The first rectangle is not labeled. The second rectangle is 5 centimeters long and 3 centimeters wide. The third rectangle is 8 centimeters long. The triangle on top of the second rectangle is labeled 5 centimeters on its base. A side of the top triangle is marked as a line between the top vertex of the triangle which is labeled upper A and the bottom right vertex which is labeled upper B. The bottom triangle is not labeled.

What is the length of AB
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(1 point)

Answer 1

To determine the length of segment AB, we can apply the Pythagorean theorem since triangle AB represents a right triangle (with the height of the triangle being the height of the rectangle it is on, and the base being the line segment labeled as 5 cm).

From the information given:
- The base of the top triangle is 5 cm (this is the length of rectangle width, as the triangle's base is on that rectangle).
- The triangle's height is equal to the height of the rectangle below it, but since it is not given directly, we assume height to be the same and can work with the information we have.

Calculating the hypotenuse (AB) requires finding its height, which is likely the width of the rectangle, in this case, 3 cm.

Using the Pythagorean theorem:
\[ AB = \sqrt{(base)^2 + (height)^2} \]
Here, base = 5 cm, and height = 3 cm:
\[ AB=\sqrt{(5^2) + (3^2)} \]
\[ AB=\sqrt{25+9} \]
\[ AB=\sqrt{34} \]
\[ AB \approx 5.83 \text{ cm} \]

Therefore, the length of segment AB is approximately \( 5.83 \text{ cm} \).