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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.

Respuesta :

ujalakhan18

Answer:

[tex]\huge\boxed{\sf w = 10}[/tex]

Step-by-step explanation:

Let the length be L and width be w.

Given that,

[tex]\displaystyle L \propto \frac{1}{w}[/tex]

Converting proportionality into equality and using the constant k.

[tex]\displaystyle L = \frac{k}{w}[/tex]    -------------------------(1)

Now, given that:

L = 2 when w = 70

Put in the above equation.

[tex]\displaystyle 2 = \frac{k}{70} \\\\Multiply \ both \ sides \ by \ 70\\\\2 \times 70 = k\\\\140 = k\\\\k = 140[/tex]

Now,

Finding w when L = 14

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

[tex]\displaystyle 14 = \frac{140}{w} \\\\w = \frac{140}{14} \\\\w = 10\\\\\rule[225]{225}{2}[/tex]

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