Answer
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
[tex]width =\frac{3\times x\times 4}{4}[/tex]
[tex]width =\frac{3x}{4}[/tex]
As given
sketchbook is 4in high .
The volume of the rectangular solid is 768 in³ .
Formula
Volume of the rectangular solid = length × breadth × height
[tex]768 = \frac{ x\times 3x\times 4}{4}[/tex]
768 = 3x²
[tex]x^{2} =\frac{768}{3}[/tex]
x² = 256
As
[tex]\sqrt{256} = 16[/tex]
x =16 in
Length = 16 in
[tex]width = \frac{3\times 16}{4}[/tex]
= 12 in
Therefore the length and breadth of the rectangular solid be 16 in and 12 in.
