Chapter 9.3, Problem 23Q

To determine

To calculate the length and width of prism.

Answer to Problem 23Q

Width is $x=4m$

Length $=16m$

Explanation of Solution

Given information:

The length of rectangular prism is four times its width Height( h ) of the prism is 5 meter

Volume( V ) of the rectangular prism $=380m^3$

Formula used:

Volume( V ) of the rectangular prism $=l\times w\times h$

Calculation:

Let x be the width of rectangular prism

Then Length will be $4x$

Substituting value of length( l ),width( w ),Height( h ) and volume( V ) of the rectangular prism in the rectangular prism volume formula,

  $380=4x\times x\times 6$

On solving

  $95=x^2\times 6$

On solving

  $x^2=\frac{95}{6}$

On solving

  $x=\pm \frac{\sqrt{570}}{6}$

On solving

  $x=\frac{\sqrt{570}}{6}$

  $x=-\frac{\sqrt{570}}{6}$

On solving

  $x\approx 3.97911$

  $x\approx -3.97911$

Width cannot be negative

Then approximate width is $x=4m$

Length $=4x$

Then

Length $=4\times 4=16m$