Question

For a given set of rectangles, the length is inversely proportional to the width. In one of these rectangles, the length is 2 and the width is 70. For this set of rectangles, calculate the width of a rectangle whose length is 14.

Answer 1

`\huge\boxed{\sf w = 10}`

Explanation:

Let the length be L and width be w.

Given that,

`\displaystyle L \propto (1)/(w)`

Converting proportionality into equality and using the constant k.

`\displaystyle L = (k)/(w)` -------------------------(1)

Now, given that:

L = 2 when w = 70

Put in the above equation.

`\displaystyle 2 = (k)/(70) \\\\Multiply \ both \ sides \ by \ 70\\\\2 * 70 = k\\\\140 = k\\\\k = 140`

Now,

Finding w when L = 14

Put L = 14 and k = 140 in Eq. (1)

`\displaystyle 14 = (140)/(w) \\\\w = (140)/(14) \\\\w = 10\\\\\rule[225]{225}{2}`