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Chapter 12: Q39. (page 480)

All nine edges of right triangular prism are congruent. Find the length of these edges if the volume is543鈥夆赌塩尘3.

Short Answer

Expert verified

The length of the edges is6 cm.

Step by step solution

01

Step 1. Given information.

All nine edges of a right triangular prism are congruent.

02

Step 2. Write the concept.

Since nine edges of a right triangular prism are congruent.

To find the edges length, let edges length isx,

So, the base area is:

b=34x2

03

Step 3. Determine the volume.

Now, the volume is:

v=bh543=34x2(x)[substitute]543=34x3[mutliply]

So,

x3=216[simplify]x=6[cuberoot]

Then, the length of the edges is 6 cm when the volume is543鈥夆赌塩尘3 .

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