The length of a rectangle with constant area varies inversely as the width. When the length is 18 ft, the width is 8 ft. How do you find the length when the width is 9 ft?

To find the length when the width is 9 ft, we can use the inverse variation formula. Inverse variation states that the product of the length and width remains constant.

Let L be the length and W be the width. We are given that when L is 18 ft, W is 8 ft. Using this information, we can set up the equation:

L * W = k

Substituting the given values, we have:

18 * 8 = k

Solving for k, we find:

k = 144

Now, we can use this value of k to find the length when the width is 9 ft. Let's call this length L2. We have:

L2 * 9 = 144

Solving for L2, we find:

L2 = 144 / 9

L2 = 16 ft

Therefore, when the width is 9 ft, the length is 16 ft.

Costant area is obtained by lenght x width, so it is 18 x 8 = 144

Inversely, you obtain the lenght by dividing the area by the width, so

This is an example of inverse proportion. The product of two quantities remains the same, in this case the area.

Thinking through the question logically we can see that if one quantity is halved the other must be doubled to keep the product the same.

So the new dimensions would be 9 feet by 16 feet.