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Answer :
Final answer:
To find the height and width of the aquarium, we converted the volume from cubic inches to gallons, established a quadratic equation using the relationship between height, width, and length along with the given volume, and solved it to find the width to be 10 inches and height to be 14 inches.
Explanation:
To find the height and the width of the 10-gal aquarium, we must first convert its volume from cubic inches to gallons. Since 1 gallon is approximately 231 cubic inches, we simply divide the aquarium's volume in cubic inches by 231 to get the volume in gallons.
2800³ in. / 231 in.³/gallon = 12.121 gallons (This should be 10 gallons as stated, so there might be a typo in the volume, but we will use the given value for the calculations).
Let's let the width of the aquarium be 'w' inches. Then the height is 'w + 4' inches. We are given that the length is 20 inches. So, we know that:
- Volume = length × width × height
2800 in.³ = 20 in. × w × (w + 4)
140 in.³ = w × (w + 4)
w² + 4w - 140 = 0
Solving the quadratic equation we get two possible solutions for w:
- w = 10 or
- w = -14 (which is not possible for the width of an aquarium)
Hence, the width is 10 inches, and the height (which is 4 inches greater than the width) is 14 inches.
The dimensions of the aquarium are 20 inches in length, 10 inches in width, and 14 inches in height.
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