Question

The area of a square and a rectangular field is equal
and is 900 m2. If the perimeter of the rectangular
field is 2 m more than that of the square field,
calculate the dimensions of the rectangular field​

Answer 1

Let the side of the square be a
Area of square=900 m^2
a^2=900
a=30m
So the side of the square is 30 m
Area of square=Area of rectangle
Area of rectangle=900 m^2
Let the dimensions of the rectangular field be length(l) and breadth(b)
We know that,
Area of rectangle=l x b
900=l x b
b=(900/l)————— 1
Now,
It is given that,
Perimeter of rectangular field=2+Perimeter of the square
2(l+b)=2+4a
2(l+b)=2+4 x 30
2(l+b)=2+120
2(l+b)=122
l+b=61
l+(900/l)=61 (From eq 1)
(l^2+900)/l=61
l^2+900=61l
l^2-61l+900=0
l^2-25l-36l+900=0
l(l-25)-36(l-25)=0
(l-25)(l-36)=0
l-25=0,l-36=0
l=25,l=36
Substituting l=25 and l=36 on eq 1
b=900/25,b=900/36
b=36,b=25
Length of rectangle=36 cm or 25 cm
Breadth of rectangle=36 cm or 25 cm