Question

A box with no top is to be constructed from a piece of cardboard whose length measures 6 inches more than its width. The box is formed by cutting squares that measure 2 inches on each side from the four corners and then folding up the sides. If the volume of the box will be 14 in^3​, what are the dimensions of the piece of ​ cardboard?

Answer 1

W=width
L=Length

Two equations

1) W+6=L
2) (W-4)*(L-4)*2=14

Solve

(W-4)*(W+6-4)*2=14

(W-4)*(W+2)*2=14

(W-4)*(W+2)=7

W^2-2W-8=7

W^2-2W-15=0

Factor

(W-5)*(W+3)=0

W-5=0

W=5

L=W+6

L=5+6

L.=11

Answer

W=5
L=11

Answer 2

This is not possible

W = width of cardboard to start with

W+6 = length of cardboard to start with

H =2 (height of finished box)

volume = W x L x H = 14 in^3

if H=2 in, then the area of the base before cutting out the 2x2 corners is W x L = 7 in^2

This is not enough area to cut out the 4 corners of 2x2 each, which would be 16 in^2