Question

The ratio of the perimeter of a square to the length of a rectangle is 5:6
The ratio of the length to the width of the rectangle is 3: 2
The perimeter of the rectangle is 60cm. Find the area of the square

Answer 1

Given :-

• The ratio of the perimeter of a square to the length of a rectangle is 5 : 6

• The ratio of the length to the width of the rectangle is 3 : 2

• The perimeter of rectangle = 60cm

To Find :-

The area of square = ?

Solution :-

The perimeter of rectangle = 2 ( L + B)

Here,

Length and Breath are in ratio = 3 : 2

Let the ratios be 3x and 2x

Therefore,

Area of rectangle = 2 ( 3x + 2x )

60 = 2 ( 5x)

60 = 10x

x = 60/10

x = 6

The length of rectangle = 3 * 6 = 18cm

The breath of rectangle = 2 * 6 = 12cm

Now,

The ratio of the perimeter of a square to the length of a rectangle is 5 : 6

Let the ratios be 5x and 6x

According to the question,

5x = 6x

5 * 6 = 6 * 6

30 = 36

Now,

we know that,

Perimeter of square = 30cm

4 * side = 30

Side = 30 / 4 = 15/2 = 7.5cm

Now,

Area of square = Side * Side

Area of square

= 7.5 * 7.5 = 56.25cm^2$.$

Answer 2

Step-by-step explanation:

$\large \star\sf\underline\blue{Question} ::-$

.

The ratio of the perimeter of a square to the length of a rectangle is 5:6

The ratio of the length to the width of the rectangle is 3: 2

The perimeter of the rectangle is 60cm. Find the area of the square

$\large \star\sf\underline \blue{To \: Find} ::-$

Area of Square?

$\large \star\sf\underline \blue{Formula} ::-$

Area of square = side × side OR side^2

$\large \star\sf\underline \red{SolutioN} ::-$

Length and Breadth are in ratio = 3:2

Let the ratio be 3y and 2y

Since

Area of Rectangle = 2(3y + 2y)

$\longrightarrow60 = 2(5y) \\ \longrightarrow60 = 10y \\ \longrightarrow \frac{60}{10} = y \\\longrightarrow \sf \fbox\red{6 = y}$

Length of Rectangle = 3 × 6 = 18cm

Breadth of Rectangle = 2 × 6 = 12cm

Ratio of the perimeter of a square are to the length of a rectangle = 3:6

Let the ratio be 5x and 6x

$\\\rightarrow 5x = 6x </p><p> \\\rightarrow 5 × 6 = 6 × 6</p><p> \\ \rightarrow30 = 36$

We know

Perimeter of square = 30cm

4 × 5 = 30

$Side = \frac{30}{4} \\ = > \frac{15}{2} \\ = > \sf \fbox \red {7.5cm}$

Area of square = side × side OR Side^2

$\rightarrow7.5 × 7.5 \\ \rightarrow\huge\sf\green{ 56.25 {cm}^{2} }$