Question

2. Find the area of a square, whose perimeter and area are in the ratio 1:2​

Answer 1

Solution :

Here, for a certain square, the perimeter and area are in the ratio of 1 : 2.

Let us assume that the side of the square is x cm in length.

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Perimeter of square :

> 4x

Area of square : x²

[ Perimeter ] : [ Area ] = 1 : 2

> 2[ Perimeter ] = [ Area ]

> 2 × 4x = x²

> x² = 8x

x ≠ 0 as a side of a square can never be 0 .

So, x = 8

Thus , the side of the square is 8 cm .

Area of the square is 64 cm² .

This is the required answer.

_________________________________________

Answer 2

${\large{\bold{\rm{\underline{Given \; that}}}}}\; \; \; \; \; \green \bigstar$

★ Perimeter and area of a square is in the ratio of 1:2

${\large{\bold{\rm{\underline{To \; find}}}}}\; \; \; \; \; \green \bigstar$

★ Area of square.

${\large{\bold{\rm{\underline{Solution}}}}}\; \; \; \; \; \green \bigstar$

★ Area of square = 64 unit sq.

${\large{\bold{\rm{\underline{Assumption}}}}}\; \; \; \; \; \green \bigstar$

★ Let a is the side of square.

${\large{\bold{\rm{\underline{Using \; concept}}}}}\; \; \; \; \; \green \bigstar$

★ Formula to find perimeter of square.

★ Formula to find area of square.

${\large{\bold{\rm{\underline{Using \; concept}}}}}\; \; \; \; \; \green \bigstar$

★ Perimeter of square = 4 × Side

★ Area of square = Side × Side

${\large{\bold{\rm{\underline{Full \; Solution}}}}}\; \; \; \; \; \green \bigstar$

~ As in the question it's already given that perimeter and area of a square is in the ratio of 1:2. And we have to find the area of square. We have to use formula to find perimeter of square and formula to find area of square. Let's solve it !..

• Area of square = a²

• Perimeter of square = 4a

~ As per the question,

• ➝ 4a/(a²) = 1/2

• ➝ 2 × 4a = a²

• ➝ 8a = a²

• ➝ a = 8

${\frak{Henceforth, \: 8 \: is \: measure \: of \: a}}$

${\frak{Henceforth, \: 8 \: is \: side \: of \: square}}$

~ Now let's find the area of square..!

• ➝ Side of square = 8

• ➝ Area of square = 8 × 8

• ➝ Area of square = 64 unit²

${\frak{Henceforth, \: 64 \: unit^{2} \: is \: area \: of \: square}}$