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:

Given :

Length of the rectangular field = 50 m

Width of the rectangular field = 30 m

Perimeter of the rectangular field is equal to perimeter of the square field.

To find :

Area of the field.

Solution :

Length of rectangular field = 50 m

Width of rectangular field = 30 m

Then,

Perimeter of rectangular field ,

= 2( Length + Width )

= 2(50+30) cm

= 2 × 80 cm

= 160 cm

Consider,

Side of square field = x m

Then,

Perimeter of square field ,

= 4 × side

= 4 × x cm

According to the question:−

Perimeter of the rectangular field is equal to perimeter of the square field.

\to\sf{4x=160}→4x=160

\to\sf{x=\dfrac{160}{4}}→x=4160

\to\sf{x=40}→x=40

Side of square field =40 cm

Formula Used :-

{\boxed{\bold{Area\:of\: square=side^2}}}Areaofsquare=side2

Then,

Area of square field = side²

→ Area of square field = 40² cm²

→ Area of square field = 1600 cm²

Therefore, the area of the square field is 1600 cm².

Answer 2

Answer:

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

_________________________

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

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

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

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

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

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

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

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

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

_________________________

$\dag \: \: \underline{\boxed{\sf Area \: of \: square \: = \: (S ide) ^{2} } \: } \: \dag \\ \\ </p><p>$

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

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

$</p><p>\therefore\:\underline{\textsf{The area of square = \textbf{1600}} \: \sf m ^{2} }</p><p>$

.