Question

The sides of a rectangular park are in the ratio 4:3. If its area is 2028 sq.m, find the cost of fencing it at rupees.3 per metre.

Answer 1

Given :-

• The sides of a rectangular park are in the ratio 4:3. If its area is 2028 sq.m.

To find :-

• Total cost of fencing rectangular park

Solution :-

• Sides of a rectangular park are in the ratio = 4 : 3

• Area of rectangular park = 2028 m²

According to question

→ Area of rectangular park = 2028

→ Length × breadth = 2028

→ 4x × 3x = 2028

→ 12x² = 2028

→ x² = 2028/12

→ x² = 169

→ x = √169

→ x = 13m

Hence,

• Length of rectangular park = 4x = 52m

• Breadth of rectangular park = 3x = 39m

Perimeter of rectangular park

→ 2(length + breadth)

→ 2(52 + 39)

→ 2 × 91

→ 182 m

The cost of fencing it at rupees 3 per metre.

→ Cost of fencing 182m rectangular park

→ 182 × 3

→ Rs.546

Therefore,

• Total cost of fencing 182m rectangular park is Rs.546

Answer 2

GIVEN :-

• Tʜᴇ sɪᴅᴇs ᴏғ ᴀ ʀᴇᴄᴛᴀɴɢᴜʟᴀʀ ᴘᴀʀᴋ ᴀʀᴇ ɪɴ ᴛʜᴇ ʀᴀᴛɪᴏ 4:3 .

• ɪᴛ's ᴀʀᴇᴀ ɪs 2028 sq.m .

• Tʜᴇ ᴄᴏsᴛ ᴏғ ғᴇɴᴄɪɴɢ ᴛʜᴇ ᴀᴇʀᴀ ɪs Rs.3 ᴘᴇʀ ᴍᴇᴛʀᴇ .

TO FIND :-

• Tʜᴇ ᴄᴏsᴛ ᴏғ ғᴇɴᴄɪɴɢ ᴏғ ᴛʜᴇ ʀᴇᴄᴛᴀɴɢᴜʟᴀʀ ᴀʀᴇᴀ .

SOLUTION :-

ʟᴇᴛ,

• $\bf\red{Length}$ = 4X

• $\bf\red{Breadth}$ = 3X

$\blue\star\:\bf\orange{Rectangular\:Area\:=\:length\times{Breadth}\:}$

⟹ 2028 = 4X × 3X

⟹ 2028 = 12X²

⟹ X² = 2028/12

⟹ X = √169

⟹ X = 13 m

Hence,

• $\bf\red{Length}$ = 4 × 13 = 52 m

• $\bf\red{Breadth}$ = 3 × 13 = 39 m

☯︎ Wᴇ ʜᴀᴠᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ, ᴡʜᴇɴ ғᴇɴᴄɪɴɢ ᴡᴏʀᴋ ᴡɪʟʟ ᴅᴏ ᴛʜᴇɴ ᴛʜᴇ ғᴇɴᴄɪɴɢ ᴅᴏ ɪɴ ᴛʜᴇ ᴘᴇʀɪᴍᴇᴛᴇʀ ᴏғ ᴛʜᴇ ʀᴇᴄᴛᴀɴɢᴜʟᴀʀ ᴘᴀʀᴋ . Sᴏ ᴡᴇ ɴᴇᴇᴅ ᴛᴏ ᴄᴀʟᴄᴜʟᴀᴛᴇ ᴛʜᴇ Pᴇʀɪᴍᴇᴛᴇʀ ᴏғ ᴛʜᴇ ᴘᴀʀᴋ .

$\pink\star\:\bf\purple{Perimeter\:=\:2\:(length\:+\:Breadth)\:}$

➳ Pᴇʀɪᴍᴇᴛᴇʀ = 2 × (52 + 39)

➳ Pᴇʀɪᴍᴇᴛᴇʀ = 2 × 91

➳ Pᴇʀɪᴍᴇᴛᴇʀ = 182 m

Now,

➪ Rᴀᴛᴇ ᴏғ ғᴇɴᴄɪɴɢ = Rs.3 ᴘᴇʀ ᴍᴇᴛʀᴇ

➟ Tᴏᴛᴀʟ ᴄᴏsᴛ = 182 × 3

➟ Tᴏᴛᴀʟ ᴄᴏsᴛ = Rs. 546

$\huge\red\therefore$ Tʜᴇ ᴄᴏsᴛ ᴏғ ғᴇɴᴄɪɴɢ ᴏғ ᴛʜᴇ ʀᴇᴄᴛᴀɴɢᴜʟᴀʀ ᴀʀᴇᴀ ɪs "Rs.546" .