Answer:
3 3/16 meters
Explanation:
The volume of the box is the product of the length and width and height. You are given the length, and you are given a relation for the width. To find the height, you need to use the given relations to create an appropriate equation to solve.
One way you can do it is this:
V = LWH
If we use a value that is (1 9/16)W, then we have ...
(1 9/16)V = L·(1 9/16)W·H . . . . . multiply the above equation by 1 9/16
Putting the given values into this relation, we have ...
(1 9/16)(12 3/4) = (2 1/2)(2 1/2)·H . . . . . . remember, 2 1/2 = (1 9/16)W
H = (1 9/16)(12 3/4)/(2 1/2)² = (1275/64)/(25/4) = 51/16
H = 3 3/16 . . . meters
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Additional comment
An alternative is to find the actual width:
(1 9/16)W = 2 1/2
W = (5/2)/(25/16) = 8/5 = 1 3/5
Then you would have ...
12 3/4 = (2 1/2)(1 3/5)·H = 4·H
H = (51/4)/4 = 51/16 = 3 3/16 . . . as above