Bimal wishes to start a $200 m^{2}$ rectanglar garden. Since he has only $45 m^{2}$ barber wire, he fences three sides of the garden letting his house compound wall act as one of the longer sides of the garden. Find the dimension of the garden.

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Solution

Area of the garden $= 200 m^{2}$
$l \times b = 200 \Rightarrow l = \frac{200}{b}$

Garden is fenced on three sides.
Length of fencing $2 b + l = 50$

$\frac{200}{l} + l = 45$
$l^{2} - 45 l + 200 = 0$
$l^{2} - 40 l - 5 l + 200 = 0$
$(l - 5) (l - 40) = 0$
$l = 40 m$ or $5 m$
$b = \frac{200}{40} = 5 m o r 200 / 5 = 40 m$

The garden is in the shape of a rectangle.

Therefore, the length and the breadth of the garden are $20 m$ and $5 m$ respectively.

Hence, this is the answer.

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Bimal wishes to start a 200 m2 rectanglar garden. Since he has only 45 m2 barber wire, he fences three sides of the garden letting his house compound wall act as one of the longer sides of the garden. Find the dimension of the garden.

Bimal wishes to start a $200 m^{2}$ rectanglar garden. Since he has only $45 m^{2}$ barber wire, he fences three sides of the garden letting his house compound wall act as one of the longer sides of the garden. Find the dimension of the garden.