Answer :
Answer:
Step-by-step explanation:
Let's solve each question step by step:
**1. A garden is 90 m long and 75 m broad. A path 5 m wide is to be built outside around it. Find the area of the path. Also find the area of the garden in hectares.**
- Dimensions of the garden:
- Length = 90 m
- Breadth = 75 m
- Width of the path = 5 m
To find the area of the path:
- Outer dimensions of the garden including the path:
- Length = 90 m + 2 × 5 m = 100 m
- Breadth = 75 m + 2 × 5 m = 85 m
- Area of the path = Area of outer rectangle - Area of garden
- Area of outer rectangle = Length × Breadth = 100 m × 85 m = 8500 sq m
- Area of garden = Length × Breadth = 90 m × 75 m = 6750 sq m
Therefore, area of the path = 8500 sq m - 6750 sq m = 1750 sq m
To find the area of the garden in hectares:
- 1 hectare = 10,000 sq m
- Area of garden in hectares = Area of garden / 10,000
- Area of garden in hectares = 6750 sq m / 10,000 = 0.675 hectares
**Answers for question 1:**
- Area of the path = 1750 sq m
- Area of the garden in hectares = 0.675 hectares
**2. A 3 m wide path runs outside and around a rectangular park of length 125 m and breadth 65 m. Find the area of the path.**
- Dimensions of the park:
- Length = 125 m
- Breadth = 65 m
- Width of the path = 3 m
To find the area of the path:
- Outer dimensions of the park including the path:
- Length = 125 m + 2 × 3 m = 131 m
- Breadth = 65 m + 2 × 3 m = 71 m
- Area of the path = Area of outer rectangle - Area of park
- Area of outer rectangle = Length × Breadth = 131 m × 71 m = 9301 sq m
- Area of park = Length × Breadth = 125 m × 65 m = 8125 sq m
Therefore, area of the path = 9301 sq m - 8125 sq m = 1176 sq m
**Answer for question 2:**
- Area of the path = 1176 sq m
**3. A picture is painted on a cardboard 8 cm long and 5 cm wide such that the margin of 1.5 cm along each of its sides. Find the total area of the margin.**
- Dimensions of the cardboard:
- Length = 8 cm
- Width = 5 cm
- Margin along each side = 1.5 cm
To find the total area of the margin:
- Outer dimensions of the cardboard including the margin:
- Length = 8 cm + 2 × 1.5 cm = 11 cm
- Width = 5 cm + 2 × 1.5 cm = 8 cm
- Area of the margin = Area of outer rectangle - Area of picture
- Area of outer rectangle = Length × Width = 11 cm × 8 cm = 88 sq cm
- Area of picture = Length × Width = 8 cm × 5 cm = 40 sq cm
Therefore, area of the margin = 88 sq cm - 40 sq cm = 48 sq cm
**Answer for question 3:**
- Total area of the margin = 48 sq cm
These are the solutions to the exercise questions.