Question

please answer fast!
If the ratio of perimeters of two squares is 4:1, find the ratio of their areas.

Answer 1

Therefore the ratio of their area will be 16:1

Answer 2

Given

Ratio of perimeters of two square is 4:1

To Find

Ratio of their areas

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

⋕Perimeter of square is 4a

⋕Area of square is a²

Where a is the side of square

$\sf= > \dfrac{Perimeter \: of \: 1st \: square}{Perimeter \: of \: 2nd \: square} = \dfrac{4a_{1}}{4a_{2}}$

$\sf = > \dfrac{4a_{1}}{4a_{2}} = \dfrac{4}{1}$

$\sf= > a_{1} = 1$

$\sf= > a_{2} = \dfrac{1}{4}$

$\sf = > \dfrac{Area \: of \: square \: 1st}{Area \: of \: 2nd \: square} = \dfrac{ {a_{1}}^{2} }{ {a_{2}}^{2} }$

$= > \dfrac{ {a_{1}}^{2} }{ {a_{2}}^{2} } = > \dfrac{ {(1)}^{2} }{( { \frac{1}{4}) }^{2} }$

$= > \dfrac{1}{ \dfrac{1}{16} } = > \dfrac{16}{1}$

Therefore,the ratio of their area is 16:1

Extra information=>

Area is Space or region which is covered by a solid object/figure it is said to be area of that object.

Area depends upon the dimensions of the figure.If dimensions is larger then larger will be the area of that object/figure and vice -versa.

PERIMETER

Perimeter is the total distance occupy by a solid 2D figure around its edge.

• A square is a quadrilateral having 4 sides & 4 vertices.
• All sides of a square are equal.
• Opposite sides of a square are parallel.
• The diagonals of a square bisects each and makes an angle of 90°
• The sum of square of Diagonals is greater than the sum of square of their sides.
• the Diagonals are also equal.