Question

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

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Answer 1

Step-by-step explanation:

Given: The side of a square = 60 m

And the length of rectangular field = 80 m

According to question,

Perimeter of rectangular field

= Perimeter of square field

= 4 side

m

Now Area of Square field

=

= = 3600 m2

And Area of Rectangular field

= length breadth = 80 40

= 3200

Hence, area of square field is larger

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Answer 2

$\huge\bf{Answer :}$

Square Field has larger area than Rectangular Field ...

$\huge\bf{Explanation :}$

For Area of Rectangle, we require Length,

Perimeter of Square = Perimeter of Rectangle

$4 \times side = 2 \: ( \: length + breadth) \\ 4 \times 60 \: m = 2(l + 80 \: m) \\ 240 \: m = 2l + 160m \\ 2l = 240 \: m - 160 \: m \\ 2l = 80 \: m \\ l = \frac{80}{2} m \\ l = 40 \: m$

Therefore, Length of Rectangle = 40 m

Now,

Area of Square -

$= {(side)}^{2} \: \\ = {(60 \: m)}^{2} \\ = 360</em></strong><strong><em>0</em></strong><strong><em> \: {m}^{2} \:$

Area of Rectangle -

$= length \times breadth \\ = 40 \: m \times 80 \: m \: \: \: \: \: \: \: \: \: \\ = 320</em></strong><strong><em>0</em></strong><strong><em> \: {m}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$area \: of \: square \: > area \: of \: rectangle \\ 360</em></strong><strong><em>0</em></strong><strong><em> \: {m}^{2} > 320</em></strong><strong><em>0</em></strong><strong><em> \: {m}^{2} \: \: \: \: \:$

Hence, Square Field has a large Area.

$\huge\bf{Thanks : ❤}$