Ex 11.4, 5 A path 1 m wide is built along the border and inside a square garden of side 30 m. Find: (i) the area of the path
Here,
Area of path = Area of larger square − Area of smaller square
Finding side of both squares
Side of larger square = 30 m
Now,
1 m path is constructed all around inside the larger square
∴ Side of smaller square = Side of larger square − 2 × 1
= 30 − 2
= 28 m
Larger square
Side = a
= 30 m
Area of larger square
= a × a
= 30 × 30
= 900 m2
Smaller square
Side = a
=28 m
Area of smaller square
= a × a
= 28 × 28
= 784 m2
Now,
Area of path = Area of larger square − Area of smaller square
= 900 − 784
= 116 m2
Ex 11.4, 5 A path 1 m wide is built along the border and inside a square garden of side 30 m. Find: (ii) the cost of planting grass in the remaining portion of the garden at the rate of Rs 40 per m2.
Now,
Grass will be planted inside the smaller square
∴ Area into which grass has to be planted = Area of smaller square
= 784 m2
Cost of planting grass in 1 m2 = Rs 40
Cost of planting grass in 784 m2 = Rs 40 × 784
= Rs 31,360
∴ Area of path is 116 m2
and it will cost Rs 31,360 to plant grass in remaining area

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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