SOLUTION: The length of the diagonal across the front of the rectangle or box is 25 diagonal across the front of the rectangle or box is 25, inches The length of the diagonal across the sid

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Question 1010553: The length of the diagonal across the front of the rectangle or box is 25 diagonal across the front of the rectangle or box is 25, inches The length of the diagonal across the side of the box is 18. The length of the three-dimensional diagnol of the box is 32 inches . What is the length of the diagnol across the top of the box?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Not both "fronts". One of them should be a different side. Think, "two sides, adjascent". Imagine the box is x from left to right, y, from up to down, and z deep (from front to back).



Every variable occurs as a square only. You can treat this simply as a linear system of three equations in three unknown variables.

I did not go further with this, but note carefully the question. It essentially asks for . Look at the last equation of the system. You can arrange this as .
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
The length of the diagonal across the front of the box is 25 inches.
The length of the diagonal across the side of the box is 18. The length of the three-dimensional of the box is 32 inches .
What is the length of the across the top of the box?
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From the condition, you have the system of three equations

 = ,      (1)
 = ,      (2)
 =    (3)

Add the equations (1) and (2) (both sides). You will get

 =    (4)

Now distract (3) from (4). You will get

 = .

Hence, y = 3 (negative root doesn't fit).

Having this, you easily find  =  from (1) and then x = 4.

Similarly, you find  =  from (2) and then z = 3.

Thus yours box has dimensions x = 4, y = 3, z = 3 inches.

Now  =  = , and  = 5 inches.

It is yours diagonal.


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