Question

A 10 gallon aquarium is 3 inches higher than it is wide. Its length is 21 inches and its volume is 2730 inches. What are the height and width of the aquarium?

Answer 1

Answer: The height and width of the aquarium are 13 inches and 10 inches respectively .

Step-by-step explanation:

Given : The volume of aquarium =  2730 cubic inches

Length of aquarium = 21 inches

Let x be the width of the aquarium,

then Height = x+3

We consider the shape of aquarium as cuboid.

Volume of Cuboid = Length x width x Height

Put values in the above formula , we get

$2730=(21)(x)(x+3)\\\\\Rightarrow\ 130=x^2+3x\\\\\Rightarrow\ x^2+3x-130=0\\\\\Rightarrow\ x^2+13x-10x-130=0\\\\\Rightarrow\ x(x+13)-10(x+13)=0\\\\\Rightarrow\(x+13)(x-10)=0\\\\\Rightarrow\ x=-13\ or\ x=10$

So , the width of aquarium =x= 10 inches  ( width cannot be negative)

So height = 10+3=13 inches.

Hence, the height and width of the aquarium are 13 inches and 10 inches respectively .