Question

the length of a rectangle exceeds its breadth by 9cm .if length and breadth each is increased by 3cm , the area of the new rectangle is 84 square cm more than the given rectangle

Answer 1

let the breadth be x

length: x+9 , breadth: x

length and breadth are incresed by 3 so,

length: x+9 +3 = x+12 ,breadth: x+3

Gn: the area of the new rectangle = 84 sq. cm

Equation:

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

x2 + 15x + 36 = 84 + x2 +9x

if we transpose x2to the opposite side then it becomes x2

x2 x2 + 15x + 36 = 84 + 9x

Now it becomes 15x+36 = 84 +9x

If we transpose 9x to the opposite side it becomes 15x +36 9x = 84

6x +36 = 84

6x = 84 36

6x= 48

x=48/6

x=8

length : 8+9 = 17

breadth= 8

Answer 2

Answer:

Let the breadth of given rectangle be xcm.

So, its length be (x+9)cm.

Area of given rectangle=(x+9)*(x).

Now,

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

And, length of new rectangle=(x+9+3)cm or (x+12)cm.

Area of new rectangle=(x+12)*(x+3).

A/q,

Area of new rectangle=84+area of given rectangle,1st process

or

(area of new rectangle)-(area of given rectangle)=84 2nd process.

I will solve it by 1st process,

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

xsq.+15x+36=84+xsq.+9x

xsq.+15x-xsq.-9x=84-36

xsq.-xsq.+15x-9x=84-36

6x=48

x=48/6

x=8

Therefore, breadth=8cm.

And, length=(8+9)cm=17cm