Question

a square field of side 65 m and rectangular field of length 75 m have the same perimeter. which field has the larger area and by how much

Answer 1

A square field side 65m
So, perimeter of square=4×65=>260m

Perimeter of square=Perimeter of rectangle
260=2(l+b)
130=l+b
130=75+b
130-75=b
55m=b


Area of square=S×S=>65×65=4225m²
Area of rectangle=l×b=>75×55=4125m²


Square has larger area
and by =4225-4125=>100m²

Answer 2

Given :

A square field of side 65 m and rectangular field of length 75 m have the same perimeter.

To Find:

which field has the larger area and by how much

Solution:

Side of square field = 65 m  

Perimeter of square field = $4 \times Side = 4 \times 65=260 m$

Length of rectangular field = 75 m  

Let the width of rectangular be x

Perimeter of rectangular field =2(l+b)=2(75+x)

So, Perimeter of square field = Perimeter of rectangular field

So, 2(75+x)=260

$75+x=\frac{260}{2}$

75+x=130

x=130-75

x= 55

width of field = 55 m  

Area of field = $Length \times Breadth = 75 \times 55 =4125 sq.m.$

Area of square field =$Side^2 = 65^2 =4225 sq.m.$

Difference in area = 4225-4125=100 sq.m.

Hence the area of square field is larger by 100 sq.m.