Question

What are the possible expressions for the dimensions of the cul
re given below?
Volume: 3x - 12x Volume: 12ky + Sky - 20k
(1)​

Answer 1

Hey dude!

Your Question is ( What are the possible expressions for the dimensions of the cuboids whose volumes are given below ?

$(1) \: \boxed{ {\bold{ volume \: : \: {3x}^{2} \: - \: 12x}}}$

Volume of Cuboid = 3x² - 12x

Volume of Cuboid = 3x(x-4)

But Volume of Cuboid = length × breadth × height

So let length = 3 , breadth = x , height = x-4

$(2) \: \boxed {\bold{volume \: : \: {12ky}^{2} \: + \: 8ky \: - \: 20k}}$

Volume of Cuboid = 12ky² + 8ky - 20k

= 4k [3y² + 2y - 5]

= 4k [3y² + (5y - 3y) - 5]

= 4k [3y² + 5y - 3y - 5]

= 4k [y[3y + 5] - 1[3y + 5]]

Volume of Cuboid = 4k(3y+5)(y-1)

But volume of Cuboid = length × breadth × height

So let length = 4k , breadth = 3y+5 , height = y-1