Question

A path 2m wide is built along the border and inside a square garden of side 40 m. Find 
(1) the area of the path
(2) the cost of planting grass in the remaining
portion of garden at the rate of
Rs 350 per m​


​

Answer 1

Answer:

Let ABCD, the square garden of side= 30 m.

PQRS is the region inside the garden.

so,

PQ = (30 -1-1 ) = 28 m

also

PS = ( 30 – 1 – 1 ) = 28 m

(i) Area of the path = Area of ABCD – Area of PQRS

= [( 30 x 30) – (28 x 28)]

= 900 – 784

= 116 sq.m

(ii) Area of the remaining portion in which the grass is planted = Area of square PQRS

= 28 x 28

= 784 sq.m

cost of planting the grass in the region PQRS = area x cost = 764 x 40

=31,360

Answer 2

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Lᴇᴛ ABCD, ᴛʜᴇ sϙᴜᴀʀᴇ ɢᴀʀᴅᴇɴ ᴏғ sɪᴅᴇ= 30 ᴍ.

PQRS ɪs ᴛʜᴇ ʀᴇɢɪᴏɴ ɪɴsɪᴅᴇ ᴛʜᴇ ɢᴀʀᴅᴇɴ.

sᴏ,

PQ = (30 -1-1 ) = 28 ᴍ

ᴀʟsᴏ

PS = ( 30 – 1 – 1 ) = 28 ᴍ

(ɪ) Aʀᴇᴀ ᴏғ ᴛʜᴇ ᴘᴀᴛʜ = Aʀᴇᴀ ᴏғ ABCD – Aʀᴇᴀ ᴏғ PQRS

= [( 30 x 30) – (28 x 28)]

= 900 – 784

= 116 sϙ.ᴍ

(ɪɪ) Aʀᴇᴀ ᴏғ ᴛʜᴇ ʀᴇᴍᴀɪɴɪɴɢ ᴘᴏʀᴛɪᴏɴ ɪɴ ᴡʜɪᴄʜ ᴛʜᴇ ɢʀᴀss ɪs ᴘʟᴀɴᴛᴇᴅ = Aʀᴇᴀ ᴏғ sϙᴜᴀʀᴇ PQRS

= 28 x 28

= 784 sϙ.ᴍ

ᴄᴏsᴛ ᴏғ ᴘʟᴀɴᴛɪɴɢ ᴛʜᴇ ɢʀᴀss ɪɴ ᴛʜᴇ ʀᴇɢɪᴏɴ PQRS = ᴀʀᴇᴀ x ᴄᴏsᴛ = 764 x 40

=31,360