Question

the length of a cuboid is 4 m more than its breadth and 6 m more than its height. if length increased by 3 m , breadth by 4 m, height decreased by 2 m its volume is increased by 512 m^3. find the dimensions of cuboid.​

Answer 1

Answer:

1.

length=x m

breadth=(x-4)m

height=(x-6)m

volume= x(x-4)(x-6)

=x(x²-10x+24)

=x³-10x²+24x

2.

length=(x+3)m

breadth=(x-4+4)m = x m

height= x-6-2 =( x-8)m

volume=(x+3)(x-8)x

=x(x²-5x-24)

= x³-5x²-24x

now...

x³-5x²-24x-512= x³-10x²+24x

5x²-48x-512=0

(x-16)(5x+32)=0

x=16(accepted)

x=-32/5(rejected)

therefore,,,

length=16

breadth=12

height=10