Question

Two rectangular fields have the same perimeter. One is a square of side 60 m, the other is a rectangle of length 7 dam. Which field has the larger area and by how many area?

Answer 1

Given

One side of a square = 60 m.

Breadth of rectangle = 15 dam

$(1dam=10m$

$1.5dam=10\times 105d)$

Now, perimeter of square = $4\times side$

$=4\times 60m$

$=240m$

$\therefore$ Two fields have same perimeter.

2(l+b)=240

$\Rightarrow 2(l+15)=240$

$\Rightarrow l+15=240/2$

$\Rightarrow l=120-15$

$\Rightarrow l=105$

Now, area of square field =$side\times side$

$=60m\times 60m$

$=3,600m^2$

Area of rectangular field =$l\times b$

$=105\times 15$

$=1575m^2$

$\therefore$ square field have the larger area by

=3600-1575=2,025 $m^2$