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18 votes
Solve with explanation please

Solve with explanation please-example-1
User Evans
by
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1 Answer

23 votes
23 votes

Answer:

Length of the rectangular lot = 60 meters

Width of the rectangular lot = 30 meters

Explanation:

Let the width of the rectangular lot be x meters.

So, Length of the same = 2x metres.


A(rectangular \:lot) = (2x)(x)


\implies A(rectangular \:lot) = 2x^2

When length is increasEd by 40 m and width by 6 m. Then....

New length =
(2x + 40) \:m

New width =
(x + 6) \:m

According to the question:


(2x + 40)(x + 6) = 2(2x^2)


\implies 2x(x + 6) + 40(x + 6) - 4x^2=0


\implies 2x^2+12x + 40x + 240 - 4x^2=0


\implies 2x^2- 4x^2+12x + 40x + 240 =0


\implies -2x^2+52x + 240 =0


\implies 2(x^2-26x - 120) =0


\implies x^2-26x - 120=0


\implies x^2-30x+4x - 120=0


\implies x(x-30)+4(x - 30)=0


\implies (x-30)(x+4)=0


\implies x-30=0,\: x+4=0


\implies x=30,\: x=-4

Since, x represents the side length, so its value can't be negative.


\implies x=30


\implies 2x=2(30)=60

Thus,

Length of the rectangular lot = 60 meters

Width of the rectangular lot = 30 meters

User Andre Artus
by
2.9k points
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