Question

The area of a rectangular garden is increased by 55 sq.m if its length is reduced by 2 m.and
the breadth is increased by 5 m. If the length is increased by 3m, and the breadth by 2 m, the
area is increased by 70 sq. m. Find the area of the rectangular garden.​

Answer 1

Step-by-step explanation:

let area of rectangular garden be x

length be y

breadth be z

x+55=2[(y-2)+(z+5)]

x+55=2[y-2+z+5]

x+55=2[y+z+3]

x+55=2y+2z+6

next

x+70=2[(y+3)+(z+2)]

x+70=2[y+z+5]

x+70=2y+2z+10

now equate this two equations

x+55=2y+2z+6

+x+70=2y+2z+10

----------------------------------

2x+125=4(y+z)+16

----------------------------------

2x+125-16=4(y+z)

2x+109=4(y+z)

109=4(y+z)÷2x

109=2(y+z)÷x

x=109÷2(y+z)

i am not getting answer

Answer 2

Answer:

Given

GivenThe area of the rectangular garden is increased by 55 sq.m if the length is reduced by 2m and breadth increased by 5m

Let the length be x

Let the breadth be y

Area =xy

According to the given information,

$(x - 2)(y + 5) = xy + 55$

$xy + 5x - 2y - 10 = xy + 55$

$5x - 2y = 65...................(1)$

and

if the length is increased by 3m and breadth by 2 m are increased by 70 sq.m

$( x + 3)(y + 2) = xy + 70$

$xy + 2x + 3y + 6 = xy + 70$

$2x + 3y = 76.............(2)$

Solving both the equations

multiplying (1) with 3 and (2) with 2 and solving

$15x - 6y = 195$

$( + )4x + 6y = 152$

$19x = 347$

$x = \dfrac{347}{19}$

$\boxed{ x = 18.2}$

substituting the value in any one equation

$\boxed{ y = 13.2}$

Area =xy=18.2×13.2=58.24 sq.m

$\boxed{area = 58.2sqm}$