Question

A square and a rectangular field with measurements as given in the figure have the same perimeter. which field has a larger area?

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Answer 1

Given :-

• Side of square = a = 60 cm

• Length of rectangle = l = 80 m

To Find :-

• Which field has larger area.

Solution :-

• Square and rectangle have same perimeter.

• Let the breadth of rectangle be 'b' m

$\pink\bigstar\:\:\bf{Perimeter \:of \:square = Perimeter \:of \:rectangle}$

$:\implies\sf{4a=2(l+b)}$

$:\implies\sf{4a=2(80+b)}$

$:\implies\sf{4\times60=2(80+b)}$

$:\implies\sf{240=160+2b}$

$:\implies\sf{2b=240-160}$

$:\implies\sf{2b=80}$

$:\implies\sf{b=\dfrac{80}{2}}$

$:\implies\sf{40\:m}$

$\therefore\bf{Breadth\:of\:rectangle=40\:m}$

Now,

$\red\star\:\sf{Area \:of \:square = a^2}$

$\longrightarrow\:\sf{60^2}$

$\longrightarrow\:\sf{60\times60}$

$\longrightarrow\:\sf{360\:m^2}$

$\red\star\:\sf{Area \:of \:rectangle = l \times b}$

$\longrightarrow\:\sf{80\times40}$

$\longrightarrow\:\sf{3200\:m}$

$\therefore\bf{Square\:has\:larger\:area.}$

Answer 2

First let us find out the perimeter of the square.

P=S×4

P=60×4

P=240m

Now the length of one sside of figure b has been given. We know that the opposite sidw is also equal.

We know that:

80×2+2x=240

=>160+2x=240

=>2x=240-160

=>x=80/2

=>x=40m

Now area of square=60×60sq.m

=3600sq.m

Now area of rectangle

=l×b

=80×40

=3200sq.m

So, area of square is bigger