Making A Box Word Problem Polynomial equations

Question

a rectangular box is to be formed by cutting squares from each corner of a rectangular piece of tin and folding up the sides. the box is to be 3 inches high, th legnth is to be twice the width, and the volume of the box is to be 96 cubic inches. Find the legnth and the width of the box. 

Answer 1

The volume is 96 in³ and the height in 3 in,

 

so the base area is 32 in²

 

the length is the is twice the width,  l = 2w

 

A = lw = (2w)w = 2 w²

 

32 in² = 2 w²

16 in² = w²

4 in = w

 

l = 2(4 in) = 8 in