Find the length of the diagonal AB:

Question

A three-dimensional rectangular prism (box) is shown.

The prism's dimensions are labeled:

* **12** along the edge from E to C.
* **4** along the edge from B to D
* **3** along the edge from C to D

The vertices of the prism are labeled with capital letters (A, B, C, D, E, F, G, H).

A dashed line connects vertex A to the vertex that meets the bottom edge where B, D, and C meet. This dashed line represents a diagonal of the rectangular prism.

(5 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.

You would first use Response area ,
on the bottom of the box rectangle to find the diagonal CB = Response area

Then use CB as Response area
of the triangle ACB, with AB being the Response area .

AB is approximately = Response area

THESE ARE THE ONLY ANSWERS FOR THE RESPONSE AREAS (UTILIZE THEM BOT)
73 cm
3cm
Area of a rectangle
Phythagorean Theorem
5cm
Square root 7
89cm
a leg
13 cm
hypotenuse
perimeter of a rectangle

Answer 1

To find the length of the diagonal AB in the rectangular prism, we can follow these steps using the provided responses.

1. Find the diagonal \( CB \): We use the dimensions of the edge lengths from B to D (4 cm) and C to D (3 cm): \[ CB = \sqrt{(4)^2 + (3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \text{ cm} \] Therefore, the response here is 5 cm.

2. Use \( CB \) as a leg of triangle \( ACB \): The length of the edge from E to C is 12 cm (which is the vertical leg of triangle ACB), thus we apply the Pythagorean theorem: \[ AB = \sqrt{(CB)^2 + (EC)^2} = \sqrt{(5)^2 + (12)^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \text{ cm} \] Therefore, the response here is 13 cm.

So, the completed response areas should be filled as follows:

• For the diagonal \( CB \): 5 cm
• For the hypotenuse \( AB \): 13 cm