SOLUTION: The diagonal, d of a box can be found using the formula d = where l, w, and h , represent the length, width and height of the box. If the box is 24 cm in length, 8 cm in width, and

Question 674558: The diagonal, d of a box can be found using the formula d = where l, w, and h , represent the length, width and height of the box. If the box is 24 cm in length, 8 cm in width, and 6 cm in height, then what is the length of the diagonal?
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!




You inadvertently left out the formula, so I'll do it without the formula
first and then again with a formula.  

We want the length of the red line DB, which is the
diagonal of the box.  

There are two right triangles ABC and DBC.

First we calculate the hypotenuse BC of right triangle
ABC using the Pythagorean theorem:

 BC� = AC� + AB�
 BC� = 8� + 24�
 BC� = 64 + 576
 BC� = 640
 BC = √640
 BC = 8√10

The required diagonal, the red line DB is the hypotenuse of
right triangle DBC.  So we use the Pythagorean theorem again

DB� = DC� + BC�
DB� = 6� + 640   (Notice we only needed BC�, not BC)
DB� = 36 + 640
DB� = 676
 DB = √676
 DB = 26

So the diagonal DB is 26 cm in length, without using the formula,
but only the Pythagorean theorem.

-----------------------------------------------

The formula you omitted is:

d = √L� + W� + H� 

Substituting gives

d = √L� + W� + H�

d = √24� + 8� + 6�

d = √576 + 64 + 36

d = √676

d = 26 cm

Edwin

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