Question

Q # 7 please solve. the math

Answer 1

The first choice is the correct answer
12 in by 22 in by 4 in

the explanation is as shown in the figure
The dimension will be x , 20 - 2x , 30 -2x

the volume= v = x(20-2x)(30-2x) = 4x³ - 100x² + 600x
differentiating with respect to x and equating to zero
dv/dx = 12x² - 200x + 600 = 0
solve for x using calculator
x = 12.7 (unacceptable)   or x = 3.92 ≈ 4

∴ The dimension will be 4 , 12 , 22

Answer 2

The answer to your question would be   4 , 12 , 22 and it is the first choice.
Solution:The dimension = x , 20 - 2x , 30 -2x
the volume=
 v = x(20-2x)(30-2x)
= 4x³ - 100x² + 600x

dv/dx = 12x² - 200x + 600 = 0x = 12.7 
 x = 3.92
≈ 4
Dimension: 4 , 12 , 22