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A rectangular prism has a length of 8, width of 9, and height of 12. What is the length of its longest internal diagonal?

AdminMod2  Sep 16, 2017

Best Answer 

 #1
avatar+7067 
+1

The longest diagonal will be from one corner to the corner completely opposite it (top and bottom, front and back, left and right). Like the black line in this picture:

 

 

We can find it's length by making it into a triangle like this:

 

 

Let's call this new gray line  " b ".

 

Now we can use the Pythagorean theorem to find  b  and  the length of the prism's diagonal.

 

92 + 82  =  b2

81 + 64  =  b2

145  =  b2

 

b2 + 122  =  (diagonal)2                 Substitute  145  in for  b2  .

145 + 122  =  (diagonal)2

145 + 144  =  (diagonal)2

289  =  (diagonal)2              Take the positive square root of both sides.

√289  =  diagonal

17  =  diagonal

hectictar  Sep 16, 2017
 #1
avatar+7067 
+1
Best Answer

The longest diagonal will be from one corner to the corner completely opposite it (top and bottom, front and back, left and right). Like the black line in this picture:

 

 

We can find it's length by making it into a triangle like this:

 

 

Let's call this new gray line  " b ".

 

Now we can use the Pythagorean theorem to find  b  and  the length of the prism's diagonal.

 

92 + 82  =  b2

81 + 64  =  b2

145  =  b2

 

b2 + 122  =  (diagonal)2                 Substitute  145  in for  b2  .

145 + 122  =  (diagonal)2

145 + 144  =  (diagonal)2

289  =  (diagonal)2              Take the positive square root of both sides.

√289  =  diagonal

17  =  diagonal

hectictar  Sep 16, 2017
 #2
avatar+86859 
+1

 

Nice diagram, hectictar....!!!

 

 

 

cool cool cool

CPhill  Sep 16, 2017

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