Question

4. A garden is 120 m long and 85 m wide. It has an inside path of uniform width 3.5 m
all around it. The remaining part of the garden is covered by grass. Find the cost of
covering the garden by grass at 50 paise per square metre.​

Answer 1

A garden is 120 m long and 85 m wide. It has an inside path of uniform width 3.5 m

all around it.

Length and Breadth of the outer rectangle = 120 m and 85 m.

And the width of the inside path is 3.5 m. (3.5+3.5=7)

Inner length of rectangle = 120 - 7 = 113 m

 

Inner breadth of rectangle = 85 - 7 = 78 m

The area of the inner rectangle = 113 × 78 = 8814 m²

Cost of covering the garden by grass = Rs 0.5 per square meter (50/100).

The total cost of covering the garden by grass (0.5 × 8814) is Rs. 4407

Answer 2

Diagram :-

$\setlength{ \unitlength}{1cm} \thicklines \begin{picture}(10,10) \put(0,0){ \line(1,0){6}} \put(0,0){ \line(0,1){3.5}} \put(6,0){ \line(0,1){3.5}} \put(0,3.5){ \line(1,0){6}} \put(0.5,0.5){ \line(1,0){5}} \put(0.5,0.5){ \line(0,1){2.5}} \put(0.5,3){ \line(1,0){5}} \put(5.5,0.5){ \line(0,1){2.5}} \put(2.75,0.7){ \sf 113 m} \put(0.7,1.6){ \sf 78 m} \put(2.6,0.8){ \vector( - 1, 0){2.1}} \put(3.8,0.8){ \vector(1,0){1.7}} \put(0.85,2){ \vector(0,1){1}} \put(0.85,1.5){ \vector(0, - 1){1}} \put(0.5,2.6){ \vector( - 1,0){0.5}} \put(0,2.6){ \vector(1,0){0.5}} \put(0.07,2.8){ \footnotesize{3.5}} \end{picture}$

Length of region covered with grass = Length of garden - 2 × Length of path $\quad$ [∵ The path is present on both sides, so we need to subtract it twice ]

⇒$\quad$ Length = 130 - 2 × 3.5

⇒$\quad$ Length = 113 m

Breadth of region covered with grass = Breadth of garden - 2 × Length of path $\quad$ [∵ The path is present on both sides, so we need to subtract it twice ]

⇒$\quad$ Breadth = 85 - 2 × 3.5

⇒$\quad$ Breadth = 78 m

We need to find the area of the grass or the area of an imaginary Rectangle whose length and breadth are 113 m and 78 m respectively.

⇒$\quad$ Area = Length × Breadth

⇒$\quad$ Area = 113 × 78

⇒$\quad$ Area = 8814 m²

Now,

⇒$\quad$ Cost = Area × 50

⇒$\quad$ Cost = 8814 × 50

⇒$\quad$ Cost = 440700 paise

Converting it into rupees , as we know,

⇒$\quad$ 1 Rupee = 100 paise

⇒$\quad$ Cost = 440700/100

⇒$\quad$ Cost = ₹ 4407

Hence, Cost of covering the grass is ₹ 4407