Respuesta :
Answer:
Length = 10 inches
Width = 10 inches
Step-by-step explanation:
The perimeter of the base is 40 inches, so we can write the following equation:
2*Length + 2*Width = 40
Length + Width = 20 (eq1)
The volume of the box is 800 in3, so we have:
800 = Length*Width*8
Length*Width = 100 (eq2)
From the (eq1), we have:
Length = 20 - Width
Using this value of Length in (eq2), we have:
(20 - Width)*Width = 100
20*Width - Width^2 - 100 = 0
Using Bhaskara's formula, we have:
Delta = b^2 - 4ac = 400 - 400 = 0
Width = -b/2a = -20/(-2) = 10 inches
Length = 20 - Width = 20 - 10 = 10 inches
So the length is 10 inches and the width is 10 inches
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
