*Q1. Find *

* (a) the area of the land*

* (b) the price of the land,*

* If the land is of rectangular shape measuring 300 m in length and 400 m in breadth. The cost of 1m ^{2} land is Rs. 10000.*

** Ans:** (a) Area = Length (

*l*) x Breadth (

*b*)

= 300 x 400

= 120000 m^{2}

(b) Cost of 1 m^{2} land = Rs 10000

Cost of 120000 m^{2 }land = 10000 x 120000 = Rs 1200000000.

*Q2. The perimeter of a park is 240m. Determine the area. *

** Ans:** Perimeter = 240 m

4 x Length of a side of the park = 240

Length of a side of park = 240/4 = 60 m

Area = (Length of a side of park)^{ 2} = (60)^{2} = 3600 m^{2 }

*Q3. The area and length of a rectangular plot of land are 1200 m ^{2} and 40 m respectively. Determine its perimeter. *

** Ans: ** Area = Length (

*l*) x Breadth (

*b*) = 1200 m

^{2}

= 40 x Breadth = 1200

= Breadth = 1200/40 = 30

Perimeter = 2 (Length (*l*) + Breadth (*b*) )

= 2 (30 + 40) = 2 (70) = 140 m

*Q4. Find the breadth and area if the perimeter and length of the rectangular sheet is 120 cm and 40 cm respectively.*

** Ans:** Perimeter = 2 (Length + Breadth) = 120 cm

2 (40 + Breadth) = 120

40 + *b *= 60

*b* = 6O – 40 =20 cm

Area = Length (*l*) x Breadth (*b*) = 40 x 20 = 800 cm^{2}

*Q5. The area of the rectangular park is equal to a square park. If the length of rectangular park measures 80m and the side of the square park is 100 m .Determine the breadth of the rectangular park. *

** Ans**: Area of the square park = (side of the park)

^{2}= (100)

^{2}= 10000 m

^{2}

Area of the rectangular park = Length (*l*) x Breadth (*b*) = 10000

80 x Breadth = 10000

Breadth = 125 m

*Q6. The length and breadth of a wire whose shape is a rectangle are 22 and 40 respectively. The wire is then reshaped into a square. Determine the side of the square and find out which shape encloses more area. *

** Ans**: Perimeter of the rectangle = Perimeter of the square

2 (Length (*l*) + Breadth (*b*)) = 4 x Side

2 (22 + 40) = 4 x Side

2 x 62 = 4 x Side

Side =124/4 = 31 cm

Area of the rectangle = 22 x 40 = 880 cm^{2}

Area of the square = (Side)^{2} = 31 x 31 = 961 cm^{2}

Therefore, the square shaped wire encloses more area.

*Q7. If the breadth and perimeter of a rectangle are 40 cm and 120 cm respectively, determine the length and area of the rectangle. *

** Ans: **Perimeter = 2 (Length (

*l*) + Breadth (

*b*)) = 120

2 (Length + 40) = 120

Length + 40 = 60

Length = 60 – 40 = 20 cm

Area = Length (*l*) x Breadth (*b*) = 20 x 40 = 800 cm^{2}

*Q8. A door is fitted in a wall whose length measures 1 m and breadth measures 2 m. The length and breadth of the wall are 5 m and 3.5 m (in the given figure). The price of white washing the wall is Rs 10 per m ^{2}. Find the cost of whitewashing the wall without the door. *

** Ans:** Area of the wall = 5 x 3.5 = 17.5 m

^{2}

Area of the door = 2x 1 = 2 m^{2}

Area to be white-washed = 17.5 – 2 = 15.5 m^{2}

Cost of white-washing 1 m^{2} area = Rs 10

Cost of white-washing 15.5 m^{2} area = 15.5 x 10 = Rs 155