A farmer wishes to start a 100 sq.m rectangular vegetable garden. Since he has only 30m barbed wire, he fences three sides of the garden letting his house compound wall act as the fourth side fencing. The dimension of the garden is

Created: 3 months ago | Updated: 3 months ago

Job Solution Janata Bank Ltd Janata Bank Ltd. || AEO (10-01-2020) || 2020 গণিত

Let, length of the garden is x meter

$∴$ Width of the garden is $\frac{100}{x}$ meter

According to question.

$x + \frac{100}{x} + x = 30 . . . . . . . . . . . . . (i) O r, \frac{100}{x} + x + \frac{100}{x} = 30 . . . . . . . . . . . . (i i) W e g e t f r o m e q u a t i o n (i) x + \frac{100}{x} + x = 30 = \frac{x^{2} + 100 + x^{2}}{x} 30 = 2 x^{2} + 100 = 30 x = 2 x^{x} - 30 x + 100 = 0 = 2 (x^{2} - 15 x + 50) = 0 = x^{2} - 15 x + 50 = 0 = (x - 10) (x - 5) = 0$

$∴$ Either x = 10

Now, if length = 10 meter

Then width = $\frac{100}{10}$ = 10 meter

Or, x = 5

Or, if length = 5 meter

Then width= $\frac{100}{5}$ = 20 meter

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