Question

1. Find the Perimeter of the rectangle whose :
i) Length = 3m
Breadth = 2m
ii) Length = 50m
Breadth = 25m
iii) Length = 150 cm
Breadth = 1 cm
iv) Length = 240 m
Breadth = 180 m

2. A farmer has a rectangular field of length and breadth 240 m and 180 m resp. He wants to fence it with 3 rounds of rope. What is the total length of rope he must use?

3. Find the distance travelled by Ajay if he takes 3 rounds of square park of side 70 m.

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Answer 1

$\bold\green{♧ \: \: Question \: 1 :}$

• Find the perimeter of the rectangle whose :

1. Length = 3m & Breadth = 2m
2. Length = 50m & Breadth = 25m
3. Length = 150cm & Breadth = 1cm
4. Length = 240m & Breadth = 180m

$\bold\green{♧ \: \: Answer \: 1 :}$

$\bold\red{◇ \: Perimeter \: of \: Rectangle = 2×(l + b)}$

1. Given,

• Length = 3 m
• Breadth = 2 m

To Find,

• Perimeter?

Solution,

Perimeter = 2 × (l + b)

⟹ Perimeter = [2 × (3 + 2)] m

⟹ Perimeter = (2 × 5) m

⟹ Perimeter = 10 m

2. Given,

• Length = 50 m
• Breadth = 25 m

To Find,

• Perimeter?

Solution,

⟹ Perimeter = [2 × (50 + 25)] m

⟹ Perimeter = (2 × 75) m

⟹ Perimeter = 150 m

3. Given,

• Length = 150 cm
• Breadth = 1 cm

To Find,

• Perimeter?

Solution,

⟹ Perimeter = [2 × (150 + 1)] cm

⟹ Perimeter = (2 × 151) cm

⟹ Perimeter = 302 cm

4. Given,

• Length = 240 m
• Breadth = 180 m

To Find,

• Perimeter?

Solution,

⟹ Perimeter = [2 × (240 + 180)] m

⟹ Perimeter = (2 × 420) m

⟹ Perimeter = 840 m

$\bold\green{♧ \: \: Question \: 2 :}$

• A farmer has a rectangular field of length and breadth 240 m & 180 m respectively. He wants to fence it with 3 rounds of rope. What is the total length of rope he must use?

$\bold\green{♧ \: \: Answer \: 2 :}$

• The farmer wants to fence his field with 3 rounds of rope. So, he has to cover three times the perimeter of that field.

First we calculate, the perimeter of the field.

Perimeter of field = 2 × (l + b)

⟹ Perimeter = [2 × (240 + 180)] m

⟹ Perimeter = (2 × 420) m

⟹ Perimeter = 840 m

Total length of rope required = 3 × Perimeter of the field

⟹ 3 × 840 m

⟹ 2520 m

$\bold\green{♧ \: \: Question \: 3 :}$

• Find the distance travelled by Ajay if he takes three rounds of square park of side 70 m.

$\bold\green{♧ \: \: Answer \: 3 :}$

Distance travelled by Ajay to take three rounds of square park = 3 × Perimeter of square.

$\bold\red{Perimeter \: of \: square = 4 × side}$

Distance travelled by Ajay = [ 3 × ( Perimeter of square)

⟹ [ 3 × (4 × 70) ] m

⟹ (3 × 280) m

⟹ 840 m

Answer 2

Answer:

1. (i) 10 m.

(ii) 150 m.

(iii) 302 cm.

(iv) 840 m.

2. Total length of rope he must use is 2520 m.

3. Distance travelled by Ajay is 840 m.

Step-by-step explanation:

We know,

• Perimeter of rectangle = 2×(length + breadth)

➊ i) Length = 3m, Breadth = 2m

$\longrightarrow$ Perimeter = 2 × (3 + 2)

$\longrightarrow$ Perimeter = 6 + 4

$\longrightarrow$ Perimeter = 10

Thus,

Perimeter of rectangle is 10 m.

ii) Length = 50m, Breadth = 25m

$\longrightarrow$ Perimeter = 2 × (50 + 25)

$\longrightarrow$ Perimeter = 100 + 50

$\longrightarrow$ Perimeter = 150

Thus,

Perimeter of rectangle is 150 m.

iii) Length = 150 cm, Breadth = 1 cm

$\longrightarrow$ Perimeter = 2 × (150 + 1)

$\longrightarrow$ Perimeter = 300 + 2

$\longrightarrow$ Perimeter = 302

Thus,

Perimeter of rectangle is 302 cm.

iv) Length = 240 m, Breadth = 180 m

$\longrightarrow$ Perimeter = 2 × (240 + 180)

$\longrightarrow$ Perimeter = 480 + 360

$\longrightarrow$ Perimeter = 840

Thus,

Perimeter of rectangle is 840 m.

➋ Given,

• Length is 240 m.
• Breadth is 180 m.

We need to find fence.

We know,

Fence = Perimeter

So,

$\longrightarrow$ Fence = 2 × (240 + 180)

$\longrightarrow$ Fence = 480 + 360

$\longrightarrow$ Fence = 840.

He fence it 3 times (or 3 rounds).

So, Total length of rope = 3 × 840

$\longrightarrow$ 2520

Thus,

Total length of rope he must use is 2520 m.

➌ Side of square park is 70 m.

He takes 3 rounds of park then,

$\longrightarrow$ Total distance travelled by Ajay = Perimeter of square park × 3

$\longrightarrow$ Total distance = (4 × 70) × 3

$\longrightarrow$ Total distance = 840

Thus,

Total distance travelled by Ajay is 840 m.