Question

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A square and a rectangular field with
measurements as given below have same perimeters. Which field has a larger areA?
• Side of square is given as 60 m
• Side of rectangle is given as 80 m

(If possible then please give diagrams too).

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Answer 1

Answer:

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Answer 2

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$\bf\huge\underline\red{Given}$

$\bf \: Side \: of \: square = a = 60 m$

$\bf \: Length \: of \: rectangle = L = 80m$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf\huge\underline\red{Let}$

$\bf \: Breadth \: of \: rectangle = b \: m$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf \huge \underline \pink{given }$

Square and rectangle field have the same perimeter

$\bf \: Perimeter \: of \: rectangle = Perimeter \: of \: square$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf2(l + b) = 4a$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf2(80 + b) = 4 \times 60$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf160 + 2b = 240$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf2b = 240 - 160$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf2b = 80$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf \: b = \frac{180}{2}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf \: b = 40m$

$\bf \: So, breadth \: of \: rectangle = 40 m$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf \huge \underline \red{now}$

$\huge \fbox \blue{area \: of \: sq.}$

$\bf \: Area = {a}^{2}$

$\bf \: p utting \: a \: = 60m$

$\bf \: area \: = ( {60})^{2}$

$\bf = 60 \times 60 = 360 {m}^{2}$

$\huge \fbox \blue{area \: of \: rect.}$

$\bf \: Area = L × B$

$\bf \: putting \: l \: = 80 \: and \: b = 40$

$\bf \: area \: = 80 \times 40$

$\bf = 3200 {m}^{2}$

$\bf \huge \underline \pink{ \: sq. \: has \: larger \: area}$

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Hope You Understand This Concept Mate :)