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What is the longest line segment that can be drawn in a right rectangular prism that is 13 cm​ long, 10 cm​ wide, and 9 cm​ tall?

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5 votes

The longest line segment that can be drawn in a right rectangular prism is the space diagonal, which connects opposite corners of the prism.

To find the length of the space diagonal of a rectangular prism, we can use the Pythagorean theorem three times, once for each face diagonal. Then, we can take the maximum value of the three face diagonals as the length of the space diagonal.

The formula for the length of a space diagonal in a rectangular prism is:

diagonal = sqrt(l^2 + w^2 + h^2)

where l, w, and h are the length, width, and height of the rectangular prism, respectively.

Substituting the given values, we get:

diagonal = sqrt(13^2 + 10^2 + 9^2) ≈ 18.247 cm

Therefore, the longest line segment that can be drawn in the right rectangular prism is approximately 18.247 cm long.

User Daleman
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4 votes

Answer: So, the longest line segment that can be drawn in the right rectangular prism is approximately 21.8 cm. Round if needed to.

Explanation:

User Aashish Nagar
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