Question

Q.6 - The length of a rectangle is thrice its breadth. If its length is
decreased by 9 cm and breadth is increased by 9 cm, the area of the
rectangle is increased by 81 sq. cm. Find the length of the rectangle.​

Answer 1

Answer:

let the breadth be x

length=3x

area=x×3x

=3x^2

length2=3x-9

breadth2=x+9

area=(3x-9)×(x+9)

3x^2+81=3x^2+27x-9x-81

18x=162

x=162/18

x=9

length=3x

length=3×9

length=27cm

Answer 2

To find:

Length of the rectangle

Given:-

length of rectangle is thrice it's breadth,lenght is decreased by 9cm and breadth is increased by 9cm and the area is increased by 81 sq. cm

Solution:-

Let the breadth be x

Then length be 3x

length is decreased by 9cm= 3x-9 cm

and breadth=x+9 cm

We know that

Area of rectangle=lenght*Breadth

$(3x - 9)(x + 9) - 3x \times x = 81$

${3x}^{2} + 27x - 9x - 81 - {3x}^{2} = 81$

$18x - 81 = 81$

$18x = 162$

$x = \frac{162}{18}$

$x = 9cm$

Therefore,

Breadth=9cm

length=3x

=3*9

=27 cm