Question

sketchbook is 4in high and shaped like a rectangular solid. the with is three-fourths as long as the length. find the length and width of the box if its volume is 768in^3

Answer 1

Find out the length and width of the box if its volume is 768in³ .

To prove

Let us assume that the length of the rectangular solid be x .

As given

the width is three-fourths as long as the length.

Than

`width =(3* x* 4)/(4)`

`width =(3x)/(4)`

As given

sketchbook is 4in high .

The volume of the rectangular solid is 768 in³ .

Formula

Volume of the rectangular solid = length × breadth × height

`768 = ( x* 3x* 4)/(4)`

768 = 3x²

`x^(2) =(768)/(3)`

x² = 256

As

`√(256) = 16`

x =16 in

Length = 16 in

`width = (3* 16)/(4)`

= 12 in

Therefore the length and breadth of the rectangular solid be 16 in and 12 in.