Question

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.

Answer 1

SOLUTION :

Given :  

Area of a rectangular mango grove = 800 m²

Let breadth of a rectangular Mangrove = x m

length of a rectangular Mangrove = 2x

[Given : length is twice its breadth]

A.T.Q,

Area of a rectangular mango grove = Length × breadth

800 m² = 2x × x

2x² = 800

x² = 800/2 = 400

x = √400

x = ±20

[Breadth can never be negative]

So, x = 20

Breadth of a rectangular Mangrove = x = 20 m

Breadth of a rectangular Mangrove = 20 m

Length of a rectangular Mangrove =2x = 2×20 = 40 m

Hence , the Length of a rectangular Mangrove= 40 m & Breadth of a rectangular Mangrove = 20 m.

∴ It is possible to design a rectangular mango grove having area 800 m² and length = 40 m & breadth = 20 m.

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Answer 2

$\boxed{\bf \: Solution}$

$\rm \: Let \: breadth \: of \: a \: rectangular \: mango \: grove = x \: m$

$\rm \: Then ,\: length \:of \: a \: rectangular \: grove=2 \: x \: m$

$\rm \: According \: to \: the \: question,$

$\rm \: Area \: of \: rectangular \: mango \: grove =800 \: m^{2}$

$\implies \: \: \: \: \: \: \: \: \: \: \rm \: 2x(x)=800 \: \: \: \: \: \: \: \: \: \: \: \: [\because \: area= \: length \times \: breadth]$

$\implies \: \: \: \: \: \: \: \: \: \: \rm \: 2x^{2} =800 \implies \: x^{2} =400 \implies \: x= \pm \: 20$

$\rm \: But, \: x=-20 \: is \: not \: possible \: because \: breadth \: can \: never \: be \: negative.$

$\rm \: So, \: x=20.$

$\rm \: Thus, \: length =2x=40 \: m \: and \: breadth = 20 \: m.$