Question

8. For a given set of rectangles, the length is inversely proportional to the width. In one of these rectangles, the length is 12 and the width is 6. For this set of rectangles, calculate the width of a rectangle whose length is 9. 25 Rotate < 3 of 4 o 416 N A

Answer 1

Answer: Width is 8

Length of a rectangle is inversely proportional to its width

Mathematically, this can be represented as

`l\text{ }\propto\text{ }(1)/(w)`

Introducing a proportionality constant K, then the expression become

`\begin{gathered} l\text{ = }\frac{k\text{ x 1}}{w} \\ l\text{ = }(k)/(w) \end{gathered}`

Find K, when l = 12 and w = 6

From the above expression, make K the subject of the formula

K = l x w

K = 12 x 6

k = 72

Find the width, when l = 9 and k = 72

Since, l = k/w

cross multiply

l x w = k

lw = k

Divide both sides by l

w = k/l

w = 72/9

w = 8

The answer is 8