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Find the length of the diagonal of a
rectangular prism. Round to the nearest tenth.
9.8 cm
14.1 cm
15.1 cm
13.7 cm

Ask by Moran Cervantes. in the United States
Mar 29,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

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The diagonal of the rectangular prism is approximately 15.1 cm.

Solución

We start by using the formula for the space diagonal of a rectangular prism with side lengths , , and :
Given the dimensions:
  • cm
  • cm
  • cm
Substitute the values into the formula:
Calculate the squares:
Add them together:
Now, take the square root:
Calculating the square root gives approximately:
Thus, the length of the diagonal of the rectangular prism is approximately cm.

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Beyond the Answer

To find the length of the diagonal of a rectangular prism, you can use the formula:
where , , and are the length, width, and height of the prism respectively. For this prism, we have:
Calculating:
So the answer is 15.1 cm.
Math can be tricky, but understanding the formula for the diagonal makes such problems more manageable. Just remember, you’re practically connecting the corners of your prism with a string!
Many real-world objects can be approximated as rectangular prisms, from shoeboxes to buildings! Knowing how to find the diagonal is super handy, especially for packing or determining structural integrity. So whether you’re designing a new gadget or just cleaning out your closet, this formula can save the day!

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