Question

31. 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

Explanation:

Let the breadth of the rectangle be x cm.

Then, the length of the rectangle is (x+9) cm.

So, area of rectangle = length x breadth =x(x+9)cm

2

Now, length of new rectangle =(x+9+3) cm =(x+12) cm and

breadth of new rectangle =(x+3) cm.

So, area of new rectangle = length × breadth =(x+12)(x+3)cm

2

According to the given condition,

(x+12)(x+3)=x(x+9)+84

⇒x

2

+12x+3x+36=x

2

+9x+84

⇒15x+36=9x+84

⇒15x−9x=84−36

⇒6x=48

⇒x=8

So, breadth of the rectangle is 8 cm and length

=8+9=17 cm.

I hope it will help you

Answer 2

Explanation:

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