The perimeter of a rectangular field …

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The perimeter of a rectangular field is 84 meters .If the breadth of the field is increased by 2 meters and it's length is decreased by 4 meters ,the area is decreased by 32sq m.Find the length and breadth of the rectangular field.

Posted by Yash Thadani 8 years, 7 months ago

CBSE > Class 08 > Mathematics

1 answers

Naveen Sharma 8 years, 7 months ago

Ans. Perimeter of Field = 84 meter

Let Length of Field = x meter

Perimeter = {tex}2(x+breadth\space of \space field ){/tex}

=> {tex}84 = 2(x+breadth\space of \space field ){/tex}

{tex}=> 42 = x+breadth\space of \space field {/tex}

{tex}=> breadth\space of \space field = (42 - x ) meter{/tex}

Old Area = {tex}x\times (42-x) = 42x - x^2{/tex}

According to Ques,

New breadth = 42 - x + 2 = (44 - x) meter

New length = (x - 4 ) meter

New Area = {tex}(44 - x) (x-4) = 44x - 176-x^2+4x {/tex}

So, New Area = Old Area - 32

=> {tex}44x - 176 -x^2 +4x = 42x-x^2 -32{/tex}

=> {tex}44x +4x - 42x -x^2 + x^2 = -32 + 176{/tex}

=> {tex}6x = 144{/tex}

=> x = 24

So, Length of Field = 24 meter

Breadth of Field = 42- 24 = 18 meter

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