A shipping box has a surface area of 369.5 in2, a height of 9.5 inches, and a width of 3 inches. What is the length of the box? Round the answer to the nearest hundredth.(1 point)
Responses
12.50 inches
12.50 inches
6.25 inches
6.25 inches
12.96 inches
12.96 inches
25.00 inches
12.96 inches
To find the length of the box, we can use the formula for surface area:
Surface Area = 2 * (length * width + length * height + width * height)
Plugging in the given values:
369.5 = 2 * (length * 3 + length * 9.5 + 3 * 9.5)
369.5 = 2 * (3length + 9.5length + 28.5)
369.5 = 2 * (12.5length + 28.5)
369.5 = 25length + 57
Subtracting 57 from both sides:
312.5 = 25length
Dividing both sides by 25:
12.5 = length
Therefore, the length of the box is 12.50 inches.
To find the length of the box, we can use the formula for the surface area of a rectangular prism:
Surface Area = 2lw + 2lh + 2wh
Given that the surface area is 369.5 in^2, the height is 9.5 inches, and the width is 3 inches, we can plug these values into the formula and solve for the length.
369.5 = 2lw + 2(9.5)(3) + 2(3)(w)
369.5 = 2lw + 57 + 6w
369.5 = 2lw + 6w + 57
Simplifying the equation, we have:
369.5 - 57 = 2lw + 6w
312.5 = 2lw + 6w
To get the length, we need to isolate it on one side of the equation. Now we can solve for length:
312.5 = 2lw + 6w
312.5 - 6w = 2lw
(312.5 - 6w)/2w = l
Using a calculator, we can substitute different values of w and solve for l. The value of l that gives a surface area of 369.5 is our answer. Let's substitute w = 6.25 inches:
(312.5 - 6(6.25))/(2(6.25)) = l
(312.5 - 37.5)/12.5 = l
275/12.5 = l
22 = l
So the length of the box is approximately 22 inches.