Question

madhu flower garden is now a square . If she enlarges it by increasing the width 1 metre and the length 3 metres the area will be 19 sq metres more than the present area . What is the length of a side now

Answer 1

WE start with assuming the initial length being x meter

The initial area = area of a square = ( length of the side ) ^2

= x^2

the width is now increased by 1 unit so new length = x+1 meter

Length is increased by 3 unit so new width = x+3

Now because length and width are not same so it becomes a rectangle

New area = area of rectangle = length x width

= ( x+3)( x+1)

Acording to question new area = initial area + 19

( x+3)( x+1) = x^2 + 19

Let us expand left side : x^2 + 3x+ 1x+ 3 = x^2 +19

x^2+ 4x + 3 = x^2+19

let us subtract x^2 from both sides . we get : 4x+3 =19

let us subtract 3 from both sides . we get : 4x = 16

let us divide both sides by 4 we get : x= (16/4)= 4

This gives initial length x= 4

Answer :

new length = x+ 3 = 4+3 = 7

new width = x+1 = 4+1 = 5

WE start with assuming the initial length being x meter

The initial area = area of a square = ( length of the side ) ^2

= x^2

the width is now increased by 1 unit so new length = x+1 meter

Length is increased by 3 unit so new width = x+3

Now because length and width are not same so it becomes a rectangle

New area = area of rectangle = length x width

= ( x+3)( x+1)

Acording to question new area = initial area + 19

( x+3)( x+1) = x^2 + 19

Let us expand left side : x^2 + 3x+ 1x+ 3 = x^2 +19

x^2+ 4x + 3 = x^2+19

let us subtract x^2 from both sides . we get : 4x+3 =19

let us subtract 3 from both sides . we get : 4x = 16

let us divide both sides by 4 we get : x= (16/4)= 4

Answer

This gives initial length x= 4

new length = x+ 3 = 4+3 = 7

new width = x+1 = 4+1 = 5