Question

the length of rectangle is 40 cm and 24 cm. if the length and the breadth varies inversely what will be the breadth of the rectangle if the length is 60 CM​

Answer 1

If the length and the breadth vary inversely then the breadth of the rectangle if the length is 60 cm will be 16 cm.

Step-by-step explanation:

Let the length of the rectangle be represented by "l" cm and the breadth be represented by "b" cm.

It is given that the length of the rectangle varies inversely with its breadth

i.e., l ∝ $\frac{1}{b}$

⇒ l = $\frac{k}{b}$ ....... (i) .......where k = constant of proportionality

Also given,

The length of the rectangle, l = 40 cm

The breadth of the rectangle, b = 24 cm

Substituting the values in (i), we get

$40 = \frac{k}{24}$

⇒ k = 40 * 24

⇒ k = 960

Now,

The length of the rectangle is given as 60 cm

So, substituting l = 60 cm and k = 960 in (i), we get

l = $\frac{k}{b}$

⇒ 60 = $\frac{960}{b}$

⇒ b = $\frac{960}{60}$

⇒ b = 16 cm

Thus, the breadth of the rectangle will be 16 cm if its length is 60 cm.

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