Question

The perimeter of a rectangle is 100m if the length is decreased by 2m and the breadth is increased by 3m , the area increases by 44m² . find the length and breadth of rectangle​.​

Answer 1

${\huge{\underline{\underline{\mathbb{\red{ANSWER}}}}}}$

$\mathtt{Length\:of\:the\:Rectangle\:=30\:m}$

$\mathtt{Breadth\:of\:the\:Rectangle\:=20\:m}$

${\underline{\bf{\green{Given\::}}}}$

The perimeter of the rectangle = 100m

If Length is decreased by 2m and

The breadth is increased by 3m , the area increases by 44m²

${\underline{\bf{\green{To\:find\::}}}}$

Length of rectangle = ?

Breadth of rectangle = ?

${\huge{\underline{\underline{\mathbb{\red{SOLUTION}}}}}}$

Let the length of the given rectangle be x m

Therefore,

Perimeter of the given rectangle = 100m

$\bf\green{perimeter\:=\:2(\:length\:+\:breadth\:)}$

=> 100 = 2(x + breadth)

=> 100/2 = x + breadth

=> 50 = x + breadth

=> Breadth = (50 - x) m

Or

$\bf\green{Area\:of\:the\:given\:rectangle\:=\:l×b}$

= x(50 - x) m²

New Length = (x-2)

New breadth = (50 - x + 3) = (53 - x) m

So,

The area of the new rectangle = (x-2)(53-x)m²

According to the given condition

Area of the new rectangle - Area of given rectangle = 44

=> (x-2)(53-x) = x(50-x)+44

=> x(53-x)-2(53-x)-x(50-x) = 44

=> 53x-x²-106+2x-50x+x² = 44

=> 53x-50x+2x-106 = 44

=> 5x = 106+44

=> 5x = 150

=> x = 150/5 = 30

Hence,

the length of the given rectangle = 30m

breadth of the given rectangle

= (50-x) = 50 - 30 = 20m

$\bf\blue{Required\:length=30m}$

$\bf\blue{Required\:breadth=20m}$

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${\huge{\underline{\underline{\mathbb{\red{VERIFICATION\::}}}}}}$

Area of the given rectangle

= 30×20 = 600m²

New length = (x-2)=(30-2) = 28m

New breadth = (53-x) = (53-30) = 23m

Area of the new rectangle - Area of the given rectangle

= (644-600)m² = 44m²

$\bf{Hence,\:verified}$