Question

Find the area of a square whose perimeter is 1000cm

Answer 1

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION \: \: } \mid}}}}}$

$\underline{ \mathfrak{ \: Given, \: }} \\ \\ \: \: \: \: \text{Perimeter of the square = 1000 cm} \\ \\ \underline{ \mathfrak{ \: To \: \: find : \: }} \\ \\ \: \: \: \: \: \: \: \: \: \text{Area of the square = ?} \\ \\ \underline{ \mathfrak{ \: Suppose, \: }} \\ \\ \: \: \: \: \: \: \: \text{Length of each side = a}$

$\underline{ \mathfrak{ \: We \: \: know \: \: that, \: }} \\ \\ \boxed{ \bold{ \pink{ \: \: Perimeter \: \: of \: \: a \: \: square = 4 \times Side \: \: }}}$

$\underline{ \bold{ \: \: A.T.Q., \: \: }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \sf{1000 = 4 \times a } \\ \\ \sf{\implies a = \frac{1000}{4}} \\ \\ \sf{ \implies a = 250} \\ \\ \tt{\therefore \: Length \: \: of \: \: each \: \: side \: \: of \: \: the \: \: square = 250 \: cm}$

$\underline{ \mathfrak{ \: We \: \: know \: \: that, \: }} \\ \\ \: \: \: \: \: \: \boxed{ \bold{ \pink{ \: Area \: \: of \: \: a \: \: square = (Side)^{2} \: }}}$

$\sf{\therefore \: Area \: \: of \: \: the \: \: square = a^{2}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ = (250 \: cm )^{2} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\sf{= 62500 \: cm^{2}} \\ \\ \tt{Hence, \: } \\ \: \: \tt{Area \: \: of \: \: the \: \: square = 62500 \: cm^{2}}$

Answer 2

Answer:

perimeter =4a

4a=1000

a =250

Step-by-step explanation:

area of square = a^2 =a×a

250×250 = 62,500