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Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m2? If so, find its length and breadth.
CBSE | Class 10 | Exercise 4.4 | Quadratic Equations
Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m2? If so, find its length and breadth.

Solution:     

Let the breadth of mango grove be l.

Length of mango grove will be 2l.

Area of mango grove =\text{ }\left( 2l \right)\text{ }\left( l \right)=\text{ }2{{l}^{2}}

2{{l}^{2~}}=\text{ }800 l2 

=\text{ }800/2\text{ }=\text{ }400

{{l}^{2~}}\text{ }400\text{ }=0

Comparing the given equation with a{{x}^{2}}~+~bx~+~c~=\text{ }0 , we get

a~=\text{ }1,~b~=\text{ }0,~c~=\text{ }400

As we know, Discriminant =~{{b}^{2}}~\text{ }4ac

=>\text{ }{{\left( 0 \right)}^{2}}~\text{ }4\text{ }\times \text{ }\left( 1 \right)\text{ }\times \text{ }\left( \text{ }\text{ }400 \right)\text{ }=\text{ }1600

Here,~{{b}^{2}}~\text{ }4ac~>\text{ }0

Thus, the equation will have real roots. And hence, the desired rectangular mango grove can be designed.

l~=\text{ }\pm 20

As we know, the value of length cannot be negative.

Therefore, breadth of mango grove = 20 m

Length of mango grove = 2 × 20 = 40 m

i

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