# 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?

Jun 16, 2016

lenght = 16

#### Explanation:

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

lenght $= \frac{144}{9} = 16$

Jun 16, 2016

Length = 16 feet.

#### Explanation:

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.

$a r e a = l \times b \Rightarrow A = 18 \times 8$

However now we have  A = ?? xx 9

Let's look at the factors: $A = \left(9 \times 2\right) \times 8$

This is the same as $A = 9 \times \left(2 \times 8\right)$

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

Otherwise we could actually work out the area and work with that, but it's not as much fun that way.
$A r e a = 18 \times 8 = 144 s q f e e t$

Length = $\frac{144}{9} = 16 f e e t$