Question

Perimeter of a rectangular field 50 m long and 30 m
wide is equal to the perimeter of a square field. Find
the area of the square field.​

Answer 1

Answer:

Area of square field =1600

Explanation:

length of rectangular field=50m

breadth of rectangular field=30m

perimeter of rectangular field=2(length+breadth)

=2(50+30)

=2×80

=160m

therefore

perimeter of square =perimeter of rectangular field

4×side = 160

side =160/4

side=40

therefore

area of square field=side×side

=40×40

1600msquare

Answer 2

Answer:

Let the Length of the side of square field be x m.

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☯

$\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$\tiny \bigstar \: \underline{\boxed{\sf Perimeter \: of \: reactangle \: = \: Perimeter \: of \: square }} \: \bigstar$

$\dag \: \: \underline{\boxed{\sf Perimeter \: of \: reactangle \: = \: 2 \: (length + \: breadth) } \: } \: \dag$

$: \implies \sf 2(50 + 30) = 4x$

$: \implies \sf 2 \: \times \: 80 \: = \: 4x$

$: \implies \sf 160 \: = \: 4 x$

$: \implies \sf x \: = \: \dfrac{160}{4}$

$: \implies \underline{ \boxed{\sf x \: = \: 40 \: \: meter}}$

$\therefore\:\underline{\textsf{The Length of side of square = \textbf{40 m}}}.$

_________________________

$\qquad\dag \: \: \underline{\boxed{\sf Area \: of \: square \: = \: (S ide) ^{2} } \: } \: \dag$

$\dashrightarrow \: \: \sf Area \: of \: square \: = \: (40) ^{2}$

$\dashrightarrow \: \: \underline {\boxed{\sf Area \: of \: square \: = \: 1600 \: m^{2} } }$

$\therefore\:\underline{\textsf{The area of square = \textbf{1600}} \: \sf m ^{2} }.$