The dimensions of the box are 6 inches, 12 inches and 10 inches
Step-by-step explanation:
There is a box, with dimensions length, width and height
- The length is twice as long as the width
- The height is 4 inches greater than the width
- The volume is 720 cubic inches
We need to find its dimensions
Assume that the width of the box is x
∵ The width of the box is x
∵ The length is twice as long as the width
- Twice means times 2
∴ The length of the box = 2(x) = 2x
∵ The height is 4 inches greater than the width
- 4 inches greater means add 4
∴ The height of the box = x + 4
∵ The volume of the box = length × width × height
∵ length = 2x , width = x , height = x + 4
∴ The volume of the box = (2x) × (x) × (x + 4)
∵ (2x) × (x) = 2x²
∵ 2x²(x + 4) = (2x²)(x) + (2x²)(4) = 2x³ + 8x²
∴ The volume of the box = 2x³ + 8x²
∵ The volume of the box is 720 inches³
∴ 2x³ + 8x = 720
- Subtract 720 from both sides
∴ 2x³ + 8x² - 720 = 0
- Use your calculator to solve the equation and find the value of x
∴ x = 6
∴ The width of the box = 6 inches
∴ The length of the box = 2(6) = 12 inches
∴ The height of the box = 6 + 4 = 10 inches
The dimensions of the box are 6 inches, 12 inches and 10 inches
Learn more:
You can learn more about volume in brainly.com/question/12497249
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