Question

the area of a square field is 8649 m2. A rectangular field whose length is twice it's breadth had its perimeter equal to the perimeter of the square field. find the area of the rectangular field

Answer 1

Hi !

Let the side of the square be "a"

we know that ,

a² = area of square

a² = 8649 m²

a = √8649

a = 93 m

Side of the square = 93 m

Perimeter of a square = 4 × side
                                   = 4 × 93 = 372 m
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length of the rectangular field = x
breadth = y

Given ,
x = 2y

Perimeter of a rectangle = 2(l+b)
                                       = 2(x + y)
                                       = 2(2y + y )
                                      = 6y

given , 
perimeter of square field = perimeter of rectangular field

6y = 372
y = 372 / 6 = 62 

x = 2y

x = 2 × 62 = 124

hence ,
length = x  = 124 m
breadth = y = 62 m

area of the rectangular field  = length × breadth
                                = 124 × 62
                                = 7688 m²

Answer 2

area of square=S×S
8649. =s²
93 =S


then,
the perimeter of square=4×93=372



let the breadth be=x
let the length be =2x

perimeter of rectangle=2(l+b)=2×3x=6x
372. = 6x
372/6. =x
62. = x

length of rectangle=62
breadth of rectangle=124


area of rectangle= l×b=62×124
area of rectangle =7688m