Question

A farmer wishes to start a $100$ square metres rectangular vegetable garden. Since he has only $30$ metres barbed wire, he fences three sides of the rectangular garden. The $4^{th}$ side of the garden is surrounded by the compound wall of his house. The dimensions of the garden is __________.

• A. $25$ m $\times 4$ m
• B. $25$ m $\times 5$ m
• C. $20$ m $\times 5$ m
• D. $20$ m $\times 4$ m

Answer 1

Answer: (C)

$20$ m $\times 5$ m

Area of garden $=$ $100$ sq. m

Let length of garden be $l$.

Let breadth of garden be $b$.

Thus, $l\times b=100$ sq. m

Also, $2l+b=30$ ....(Since, $3$ sides are fenced.)

$\Rightarrow b=30-2l$

Putting in upper equation:

$l\times (30-2l)=100$

$\Rightarrow 30l-2l^2=100$

$\Rightarrow l^2-15l+50=0$

$\Rightarrow l^2-5l-10l+50=0$

$\Rightarrow (l-5)(l-10)=0$

So, when $l=5$ m:

$b=30-10=20$ m

When $l=10$ m

$b=30-20=10$ m

Thus we have $2$ possibilities.