Question

The length of a rectangle exceeds its breadth by 4 cm. If length and breadth
are increased by 7 cm and 3 cm respectively, then 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

Answer 1

Answer:

Answer:

The length and breadth are 14 cm and 10 cm

Step-by-step explanation:

Given that the length of a rectangle exceeds its breadth by 4 cm .if length and breadth are each is increased by 3 cm , the area of the new rectangle is 81 square cm more than the given rectangle.

we have to find the length and breadth of rectangle.

Let the breadth of rectangle be x cm

∴ The length is x+4

Area=length \times breadth=x(x+4)=x^2+4xArea=length×breadth=x(x+4)=x

2

+4x

Now, length and breadth are each is increased by 3 cm

New length=(x+4)+3=x+7

New breadth=x+3

\text{New area=}(x+7)(x+3)=(x^2+10x+21) cm^2New area=(x+7)(x+3)=(x

2

+10x+21)cm

2

As the area of the new rectangle is 81 square cm more than the given rectangle.

⇒ x^2+10x+21=(x^2+4x)+81x

2

+10x+21=(x

2

+4x)+81

10x-4x=81-2110x−4x=81−21

6x=606x=60

x=\frac{60}{6}=10 cmx=

6

60

=10cm

∴ Length=x+4=10+4=14 cmLength=x+4=10+4=14cm

Breadth=x=10 cmBreadth=x=10cm

The length and breadth are 14 cm and 10 cm

Step-by-step explanation:

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Answer 2

Given:-

• Length of a rectangle exceeds its breadth by 4 cm
• If length and breadth of the rectangle are increased by 7 cm and 3 cm respectively, then the area of the new rectangle will be 81 cm² more than that of the given rectangle.

To Find:-

• The length and breadth of the given rectangle.

Assumption:-

• Let the breadth be x
• Length = x + 4

Solution:-

Let us first find the area of the original rectangle,

We know,

• Area of rectangle = Length × Breadth

Hence,

Area of original rectangle = x(x + 4)

⇒ Area = x² + 4x

∴ Area of the original rectangle is x² + 4x.

Now,

For new rectangle,

Length is increased by 7 cm

Hence,

• Length = x + 4 + 7 = x + 11

Breadth is increased by 3 cm

Hence,

• Breadth = x + 3

Now,

Area of new triangle = Area of original triangle + 81

Hence,

(x + 11)(x + 3) = x² + 4x + 81

⇒ x² + 3x + 11x + 33 = x² + 4x + 81

Take x² from RHS to LHS,

⇒ x² - x² + 14x + 33 = 4x + 81

⇒14x + 33 = 4x + 81

Take variables on LHS and constants on RHS,

⇒ 14x - 4x = 81 - 33

⇒ 10x = 48

⇒ x = 48/10

⇒ x = 4.8

Let us put the value of x in the length and breadth we assumed:-

Length = x + 4 = 4.8 + 4 = 8.8 cm

Breadth = x = 4.8 cm

Therefore,

• Length of rectangle = 8.8 cm
• Breadth of rectangle = 4.8 cm

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