Question

Is it possible to design a rectangular mango grove whose length is twice its breadth and area is $800m^2$ ? If so, find its length and breadth.

• A. The rectangle is possible and it has breadth $=$ $10$ m and length $=$ $50$ m
• B. The rectangle is possible and it has breadth $=$ $30$ m and length $=$ $60$ m
• C. The rectangle is possible and it has breadth $=$ $20$ m and length $=$ $40$ m
• D. The rectangle is possible and it has breadth $=$ $20$ m and length $=$ $90$ m

Answer 1

Answer: (C)

The rectangle is possible and it has breadth $=$ $20$ m and length $=$ $40$ m

Let $x$ be the breadth and $2x$ be the length of the rectangle.

Area of the rectangle $=$ (length $\times$ breadth)
$\Rightarrow 2x\times x=800$

$\Rightarrow 2x^2=800$

$\Rightarrow x^2=\frac{800}{2}$

$\Rightarrow x^2=400$

$\Rightarrow x^2=\pm \sqrt{400}$

$\Rightarrow x=20$

Therefore, breadth $=20$ meters and length $=2\times 20=40$ meters.