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

SOLUTION :

$given \: length \: of \: rectangular \: field \: = 50m \\ \\ width \: of \: rectangular \: field \: = 30m \\ \\ perimeter \: of \: rectangle = 2(l + b) = 2(30 + 50) \\ \\ = 2(80) = 160 \: m \\ \\ perimeter \: of \: square \: field \: = 4 \times side \\ \\ according \: to \: the \: question \: \\ \\ 160 = 4 \times side \\ \\ = > side \: = \frac{160}{4} = 40 \: m \\ \\ \: thus \: length \: of \: side \: of \: square \: = 40 \: m \\ \\ area \: of \: square \: = (side) {}^{2} = (40) {}^{2} = 1600 \: m {}^{2}$

Answer 2

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

= 4x cm

${\underline{\sf{According\:to\:the\: question:-}}}$

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

$\to\sf{4x=160}$

$\to\sf{x=\dfrac{160}{4}}$

$\to\sf{x=40}$

• Side of square field =40 cm

Formula Used :-

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

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.