Question

a rectangular field is 90 M long and 60 M wide and another field is in square shape if the perimeter of both the field is same this field has greater area and by how much

Answer 1

length of the field=90m
breadth of the field=60m

Perimeter of the rectangular field=2( l + b )
=2( 90m + 60m )
=180 + 120m
=300m

It is given that, perimeter of the rectangular field is same as the square field

Perimeter of the square field= 4a { a is a side }
=>300m = 4a
=>300/4m = a
=> 75m = a

Area of the rectangular field= length × breadth
= 90m × 60m
= 5400m²

Area if the square= a²
= (75m)²
= 75m × 75m
= 5625m²
Therefore, square field has greater area than the rectangular field by 5625m² - 5400m²=225m²

Answer 2

perimeter of rectangle = 2×(90+60)
=300
perimeter of square = 4a
300 = 4a
a = 300/4
= 75
area of square = a×a
= 75×75
= 5625
area of rectangle = l×b
= 90×60
= 5400
the area difference = 5625 _ 5400
= 225