Question

One dimension of a cube is increased by 1 inches to form a rectangular block.supposed that the volume of the new block is 150 cubic inches.

find the length of an edge of the origin

Answer 1

Hello,

Let's x the side of the cube
Volume of the cube=x^3
Volume of the rectangular block :(x+1)x²=150

So x^3+x^2-150=0
==>x^3-5x^2+6x^2-30x+30x-150=0
==>x^2(x-5)+6x(x-5)+30(x-5)=0
==>(x-5)(x^2+6x+30)=0
The trinome has no real roots.

==>x=5 (in)
Proof: (5+1)*5*5=25*6=150

Answer 2

Length of edge of original block =5 inches

Explanation:

We are given that one dimension of a cube is increased by 1 inches to form a rectangular block.

Volume of new block means rectangular block=150 cubic inches

We have to find the value of edge of the original block

Let edge length of original block=x

Length of rectangular block=x+1

Breadth of rectangular block=x

Height of rectangular block=x

Volume of rectangular block=
`length* breadth* height`

Substitute the values then we get

`150=(x+1)* x* x`

`x^2(x+1)=150`

`x^3+x^2=150`

`x^3-5x^2+6x^2-30x+30x-150=0`

`x^2(x-5)+6x(x-5)+30(x-5)=0`

`(x-5)(x^2+6x+30)=0`

`x-5=0`

x=5 and
`x^2+6x+30=0`

For second quadratic equation

`D=b^2-4ac`

`D=(6)^2-4* 1* 30`

`D=36-120=-84<0`

Therefore, the roots of second quadratic equation are imaginary .

It is not possible, because we are finding length of edge of original block. Length is always is a natural number.

So, we take x=5 only

Hence,length of an edge of original block=5 inches