Question

the length and breadth of rectangular field of birati mahajati sangha are in the ratio 4:3. the path a 336 meters is covered by walking once round the field. let us write by calculating the area of the field​

Answer 1

Given:

• Ratio of Length and Breadth = 4:3
• Walking around the field = Perimeter = 336 m

To find:

➜ Area = ?

Method:

Let the length and breadth of the field be 4x and 3x respectively.

Perimeter = 2(l + b)

⇒ 336 = 2(4x + 3x)

⇒ 336 ÷ 2 = 4x + 3x

⇒ 168 = 7x

⇒ x = 168 ÷ 7

∴ x = 24 m

Now let's find the length and breadth.

Length = 4x = 4(24) = 96 m

Breadth = 3x = 3(24) = 72 m

Area = Length × Breadth

→ Area = 96 m × 72 m

∴ Area = 6912 m²

∴ Area of Birati Mahajati Sangha = 6912 m²

Answer 2

Given:-

• The ratio of length and breadth is 4:3.
• Distance covered by walking once round to the field.

⠀

To find:-

• The area of field?

⠀

Solution:-

Let,

• Length of rectangular field be 4x.
• Breadth of rectangular field be 3x.

⠀

★ Formula used:-

$\star{\boxed{\sf{\orange{Perimeter\: of\: rectangle = 2(l + b)}}}}$

⠀

$\large{\tt{\longmapsto{336 = 2(4x + 3x)}}}$

⠀

$\large{\tt{\longmapsto{336 = 2 \times 7x}}}$

⠀

$\large{\tt{\longmapsto{\dfrac{336}{2} = 7x}}}$

⠀

$\large{\tt{\longmapsto{168 = 7x}}}$

⠀

$\large{\tt{\longmapsto{\dfrac{168}{7} = x}}}$

⠀

$\boxed{\large{\tt{\longmapsto{\red{x = 24\: m}}}}}$

⠀

★ Finding the length and breadth of rectangular field.

$\large{\tt{\longmapsto{Length = 4x = 4 \times 24 = 96}}}$

⠀

$\large{\tt{\longmapsto{Breadth = 3x = 3 \times 24 = 72}}}$

⠀

Now,

• Let's, find the area of the field.

$\large{\tt{\longmapsto{Area = 96 \times 72}}}$

⠀

$\boxed{\large{\tt{\longmapsto{\red{Area = 6912\: m^2}}}}}$

⠀

Hence, the area of the field is 6912 m².

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬