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What are the possible expressions for the dimensions of the cuboids whose volumes are given below? I Volume: - 12% I I Volume: 12ky2 + 8ky - 20k I u1 Ui>

What are the possible expressions for the dimensions of the cuboids whose volumes are given below? I Volume: - 12% I I Volume: 12ky2 + 8ky - 20k I u1 Ui>

Grade:12th pass

2 Answers

Pawan Prajapati
askIITians Faculty 60782 Points
2 years ago
(i) Volume = 3%2 - 12.% = 3xC% - 4) Possible dimensions are 3, x and (x •- 4). (ii) Volume = 12ky2 + Bky - 20k = 4k(Sy2 + 2y - 5) = 4k(Sy2 + 5y - Sy - 5) "" 4k { y(3y + 5) - 1(3y + 5)1 = 4k( y - 1)(3y + 5). Poesible dimensions are 4k, y - 1and 3y + 5. CJa
Ram Kushwah
110 Points
2 years ago
Given that
Volume V = 12ky²+8ky-20k
 
Taking 4k as common
 
V=4k( 3y²+2y-5)
 
= 4k ( 3y²+5y-3y-5)
=4k { y(3y+5)-(3y+5) }
 
V = 4k (3y+5) ( y-1)........................................(1)
 
We know that the volume of acuboid is given by
 
 V = lbh= Length x Breadth x Height …........(2)
On comparision of eqn (1) and (2) we get
 
Length = 4k
Breadth = 3y+5
Height = y-1
 

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