First let's identify the givens in this problem.

Box 1 is a square so it has equal measurements for the length and width, therefore . . .

Box 1 has length = 10, width = 10, and height = 4

Box 2 has length = unknown, width = 10, and height = 5

Volume for Box 2 is 2 times the Volume for Box 1, so **V**_{2}**=2V**_{1}

The formula for the volume of a rectangular prism (i.e. a box) is length times width times height **(V = lwh)**,

so V_{1} = l_{1}w_{1}h_{1} or **V**_{1}** = (10)(10)(4)** **= 400 units**

and V_{2 }= l_{2}w_{2}h_{2} or **V**_{2}** = (x)(10)(5)** **= 50x units, with x representing the unknown length of Box 2**

Substitute these values into the given statement **V**_{2 }**= 2V**_{1 }**to get 50x = 2(400)**

Solve for x

50x = 2(400)

50x = 800

x = 16

**The height for Box**_{2}** is 16 units.**