Question

The sides of two squares are in the ratio of 5 : 7. Find the ratio of their areas and perimetre.​

Answer 1

What we have to do ?

We have provided two squares with the ratio of their sides be 5 : 7. We have to find out the ratio of their areas and perimeter.

For that, first we will consider the sides be in terms of variable then we will find perimeter and area of both the square and thereafter the ratios respectively.

Let's Solve it :

Formulae need to know :

• ${\boxed{\sf{Perimeter \: of \: square = 4 \times Side}}}$
• ${\boxed{\sf{Area \: of \: square = (Side)^{2}}}}$

Lets consider the side of first square be 5x and side of second square be 7x respectively.

For Perimeter of first square :

• Side → 5x

$\dashrightarrow\:\:\sf Perimeter \: of \: first \: square = 4 \times Side$

$\dashrightarrow\:\:\sf Perimeter \: of \: first \: square = 4 \times 5x$

$\dashrightarrow\:\:\bf Perimeter \: of \: first \: square = 20x$

For Perimeter of second square :

• Side → 7x

$\dashrightarrow\:\:\sf Perimeter \: of \: Second \: square = 4 \times Side$

$\dashrightarrow\:\:\sf Perimeter \: of \: Second \: square = 4 \times 7x$

$\dashrightarrow\:\:\bf Perimeter \: of \: Second \: square = 28x$

Hence, Ratio of their Perimeter be :

$:\implies \sf Ratio = \dfrac{Perimeter \: of \: first \: square}{Perimeter \: of \: Second \: square}$

$:\implies \sf Ratio = \dfrac{20x}{28x}$

$:\implies \sf Ratio = \dfrac{5}{7}$

$\dashrightarrow\:\: \underline{ \boxed{\sf Ratio \: of \: their \: perimeter = 5 : 7}}$

___________________________

For Area of Square 1 :

• Side → 5x

$:\implies \sf Area \: of \: first \: square = (Side)^{2}$

$:\implies \sf Area \: of \: first \: square = (5x)^{2}$

$:\implies \bf Area \: of \: first \: square = 25x^{2}$

For Area of Square 2 :

• Side → 7x

$:\implies \sf Area \: of \: second \: square = (Side)^{2}$

$:\implies \sf Area \: of \: second \: square = (7x)^{2}$

$:\implies \bf Area \: of \: second \: square = 49x^{2}$

Hence, Ratio of their Area be :

$\dashrightarrow\:\:\sf Ratio = \dfrac{Area \: of \: first \: square}{Area \: of \: second \: square}$

$\dashrightarrow\:\:\sf Ratio = \dfrac{25x^{2}}{49x^{2}}$

$\dashrightarrow\:\:\sf Ratio = \dfrac{25}{49}$

$:\implies \underline{ \boxed{\sf Ratio \: of \: their \: Area = 25 : 49}}$

Answer 2

Let side of first square = 5x

And, side of second square = 7x

Therefore,

Area of first square = 25x²

And, area of second square = 49x²

Ratios of areas = 25x² / 49x² = 25/49

Hope it helps uh !!