Question

The dimensions of portable kennel can be expressed as width x, height x-0.2 and length x+0.4.What are dimensions of portable kennel with a volume of 7.4 ft^3?Use a graphing calculator to solve.

Answer 1

Assuming the portable kennel is a box (rectangular prism), the volume is:

`V=WHL`

Where W is the width, H is the height, and L is the length.

We are given the values:

W = x

L = x + 0.4

H = x - 0.2

The volume is:

`V=x(x+0.4)(x-0.2)`

The volume is known to be 7.4, thus:

`x(x+0.4)(x-0.2)=7.4`

We cannot directly solve the equation by algebraic methods, so we use a graph. Define the function:

`y=x(x+0.4)(x-0.2)-7.4`

We need to find the value of x that makes the value of y equal to 0.

The graph of the function is shown below:

We can see the solution for x is a value near x = 1.8. Zooming the graph around the solution:

Now we have a more accurate solution at x = 1.9.

The dimensions of the kennel are:

W = 1.9

L = 1.9 + 0.4 = 2.3

H = 1.9 - 0.2 = 1.7

Checking: 1.9 × 2.3 × 1.7 = 7.43

The volume is approximately equal to 7.4