Math, asked by Anonymous, 6 days ago

The Length of a rectangle exceeds its breadth by 4 cm. If Length and Breadth are each increased by 3 cm, the area of the new rectangle will be 81 cm² more than that of the given rectangle. Find the length and breadth of the given rectangle.​

Answers

Answered by tennetiraj86
6

Step-by-step explanation:

Given :-

The Length of a rectangle exceeds its breadth by 4 cm. If Length and Breadth are each increased by 3 cm, the area of the new rectangle will be 81 cm² more than that of the given rectangle.

To find :-

Find the length and breadth of the given rectangle?

Solution :-

Let the breadth of the rectangle be X cm

Then , the length of the rectangle

= Breadth + 4 cm

= (X + 4) cm

We know that

Area of a rectangle = lb sq.units

Area of the given rectangle

= (X+4) × X cm²

=> (X×X) +(4×X)

=> X²+4X cm²

Area of the given rectangle =(X²+4X) cm²---(1)

If the length is increased by 3 cm then

The length of the new rectangle

= X+4+3

= (X+7) cm

If the breadth is Increased by 3 cm then

The breadth of the new rectangle

= (X+3) cm

Area of the new rectangle

= (X+7)×(X+3) cm²

=> X×(X+3) + 7×(X+3)

=> X²+3X+7X+21

=> X²+10X+21 cm²

Area of the new rectangle=(X²+10X+21) cm²---(2)

Given that

If length and breadth are each increased by 3 cm, the area of the new rectangle will be 81 cm² more than that of the given rectangle.

=> Area of the new rectangle = Area of the given rectangle + 81 cm²

=> X²+10X+21 = X²+4X+81

=> 10X+21 = 4X+81

=> 10X-4X = 81-21

=> 6X = 60

=> X = 60/6

=> X = 10 cm

Therefore, Breadth = 10 cm

Length = X+4 = 10+4 = 14 cm

Answer:-

The length of the given rectangle = 14 cm

The breadth of the given rectangle = 10 cm

Check :-

Length = 14 cm

Breadth = 10 cm

Length = 10+4 cm

Length = Breadth + 4 cm

Area of the rectangle = 14×10 = 140 cm²

If the length and breadth is Increased by 3 cm each then they will be 14+3 =17 cm

and 10+3 = 13 cm

Area of the new rectangle = 17×13 = 221 cm²

New area = 221 cm²

=> New Area = 140+81

=> New Area = Area of the given rectangle +

81 cm²

If length and breadth are each increased by 3 cm, the area of the new rectangle will be 81 cm² more than that of the given rectangle.

Verified the given relations in the given problem.

Used formulae:-

  • Area of a rectangle = lb sq.units

  • l = length of a rectangle

  • b = breadth of a rectangle
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