Answer: The worker would need to input Length: 10 inches and Width: 10 inches
Step-by-step explanation: The boxes as described in the question have a volume of 800 cubic inches. The height is given as 8 inches and the base length and width is not given, however the perimeter is given as 40 inches. This gives us a clue as to the dimensions of the base length and width as follows;
Perimeter = 2(L + W)
40 = 2(L + W)
40/2 = L + W
20 = L + W ---------- (1)
This means the addition of the length and width gives us a total of 20 inches.
However, note that the volume of the box is derived as;
Volume = L x W x H
With the volume and height already given as 800 and 8 respectively, the formula becomes;
800 = L x W x 8
Divide both sides of the equation by 8
100 = L x W ----------(2)
We can now solve for the pair of simultaneous equations as follows;
20 = L + W ----------(1)
100 = L x W ----------(2)
From equation (1), L = 20 - W
Substitute for the value of L into equation (2)
100 = (20 - W) * W
100 = 20W - W²
Collect like terms and you now have
W² -20W + 100 = 0
By factorization we can solve the above quadratic equation as;
(W - 10W) ( W - 10W) = 0
W - 10 = 0
W = 10
From equation (1), when W = 10, then
20 = L + 10
Subtract 10 from both sides of the equation
10 = L
Therefore, the worker would have to input, Length : 10 inches, and Width : 10 inches
