Question

The area of the square field is 5184 m2

. A rectangular field whose length is twice its
breadth, has its perimeter equal to the perimeter of the square field. Find the area of the
rectangular field.

Answer 1

• Area of rectangular field is 4608 m².

Step-by-step explanation:

Given:-

• Area of square field is 5184 m².

To find:-

• Area of rectangular field.

Solution:-

Given that,

Length of rectangular field is twice the breadth of rectangular field.

So,

Let, Breadth of rectangular field be x.

And, Length of rectangular field be 2x.

• We will find side of square field for perimeter of square field.

Area of square = Side × Side

$\longrightarrow$ (Side)² = 5184

$\longrightarrow$ Side = √5184

$\longrightarrow$ Side = 72

Side of square field is 72 m.

Perimeter of square = 4×Side

$\longrightarrow$ 4 × 72

$\longrightarrow$ 288

Perimeter of square field is 288 m.

• It is given that perimeter of square field is equal to the perimeter of rectangular field.

So, Perimeter of rectangular field is 288 m.

Perimeter of rectangle = 2(length + Breadth)

$\longrightarrow$ 288 = 2×(2x + x)

$\longrightarrow$ 288 = 4x + 2x

$\longrightarrow$ 288 = 6x

$\longrightarrow$ 288/6 = x

$\longrightarrow$ 48 = x

Or, x = 48

We have taken breadth be x. So, Breadth of rectangular field is 48 m.

We have also taken Length be 2x = 2 × 48 = 96. So, Length of rectangular field is 96 m.

Area of rectangle = length × breadth

$\longrightarrow$ 96 × 48

$\longrightarrow$ 4608

Area of rectangular field is 4608 m².

Answer 2

Answer:

$\huge \bf \: solution$

$\sf \: first \: we \: have \: to \: find \: its \: side$

$\sf \: {area}^{2} = side \: \times side$

$\sf \: side \: = \sqrt{5184}$

$\sf \: side \: = 72$

Perimeter of square = 4 × side

$\sf \: perimeter \: = 4 \times 72$

$\sf \: perimeter \: = 288 \: cm$

Now it is given that perimeter of square = perimeter of rectangle.

$\sf \therefore \: perimeter \: of \: rectangle = 2(l + b)$

$\sf \: 288 = 2(2x + x)$

$\sf \: 288 = 4x + 2x$

$\sf \: 288 = 6x$

$\sf \: x = \dfrac{288}{6}$

$\sf \: x \: = 48$

$\bf \: breadth \: = 48 \: and \: \: length \: = 2(48) = 96$

$\sf \: area \: = l \times b$

$\sf \: area \: = 96 \times 48$

$\huge \bf \: 4608 \: cm ^{2}$