RS Aggarwal Solutions: Mensuration - 1 | Mathematics (Maths) Class 7 PDF Download

 Page 1


Question 1.
RS Aggarwal Solutions Class 7 Chapter 20 - Mensuration  (Ex 20A) Exercise 20A 
  
 
  
   
 
 
  
 
Solution:
 
 
(i) Length = 24.5 m 
Breadth = 18 m 
 ? Area of the rectangle = Length × 
Breadth 
= 24.5 m × 18 m 
 = 441 m
2 
 
 
(ii) Length = 12.5 m 
Breadth = 8 dm = (8 × 10) = 80 cm = 0.8 m     [since 1 dm = 10 cm and 1 
m = 100 cm] 
 ? Area of the rectangle = Length × Breadth 
= 12.5 m × 0.8 m 
= 10 m
2 
 
 
Page 2


Question 1.
RS Aggarwal Solutions Class 7 Chapter 20 - Mensuration  (Ex 20A) Exercise 20A 
  
 
  
   
 
 
  
 
Solution:
 
 
(i) Length = 24.5 m 
Breadth = 18 m 
 ? Area of the rectangle = Length × 
Breadth 
= 24.5 m × 18 m 
 = 441 m
2 
 
 
(ii) Length = 12.5 m 
Breadth = 8 dm = (8 × 10) = 80 cm = 0.8 m     [since 1 dm = 10 cm and 1 
m = 100 cm] 
 ? Area of the rectangle = Length × Breadth 
= 12.5 m × 0.8 m 
= 10 m
2 
 
 
RS Aggarwal Solutions Class 7 Chapter 20 - Mensuration  (Ex 20A) Exercise 20A 
  
 
  
   
Solution:
 
Length of rectangular plot (l) = 48m
 
and its diagonal = 50m
 
 
Question 3.
 
 
Solution:
 
Ratio in the sides of a rectangle = 4 : 3
 
Area = 1728 cm²
 
Let length = 4x,
 
then breadth = 3x
 
Area = l x b
 
1728 = 4x x 3x
 
?
 
12x² = 1728
 
?
 
x² = 144 = (12)²
 
?
 
x = 12
 
Length = 4x = 4 x 12 = 48 m
 
and breadth = 3m = 3 x 12 = 36m
 
Question 2.
Page 3


Question 1.
RS Aggarwal Solutions Class 7 Chapter 20 - Mensuration  (Ex 20A) Exercise 20A 
  
 
  
   
 
 
  
 
Solution:
 
 
(i) Length = 24.5 m 
Breadth = 18 m 
 ? Area of the rectangle = Length × 
Breadth 
= 24.5 m × 18 m 
 = 441 m
2 
 
 
(ii) Length = 12.5 m 
Breadth = 8 dm = (8 × 10) = 80 cm = 0.8 m     [since 1 dm = 10 cm and 1 
m = 100 cm] 
 ? Area of the rectangle = Length × Breadth 
= 12.5 m × 0.8 m 
= 10 m
2 
 
 
RS Aggarwal Solutions Class 7 Chapter 20 - Mensuration  (Ex 20A) Exercise 20A 
  
 
  
   
Solution:
 
Length of rectangular plot (l) = 48m
 
and its diagonal = 50m
 
 
Question 3.
 
 
Solution:
 
Ratio in the sides of a rectangle = 4 : 3
 
Area = 1728 cm²
 
Let length = 4x,
 
then breadth = 3x
 
Area = l x b
 
1728 = 4x x 3x
 
?
 
12x² = 1728
 
?
 
x² = 144 = (12)²
 
?
 
x = 12
 
Length = 4x = 4 x 12 = 48 m
 
and breadth = 3m = 3 x 12 = 36m
 
Question 2.
RS Aggarwal Solutions Class 7 Chapter 20 - Mensuration  (Ex 20A) Exercise 20A 
  
 
  
   
Now perimeter = 2 (l + b) = 2 (48 + 36) m = 2 x 84 = 168 m 
Rate of fencing = Rs. 30 per metre 
Total cost= 168 x 30 = Rs. 5040 
Question 4.
 
 
Solution: 
Area of rectangular field = 3584 m² 
Length = 64 m 
Area = 3584 
Breadth = Area / Length = 3584/64 = 56 m 
Now perimeter = 2 (l + b) = 2 (64 + 56) m = 2 x 120 = 240 m 
Distance covered in 5 rounds = 240 x 5 = 1200 m 
Speed = 6 km/h 
Time take = 1200/100 x 60/ 6  
= 12 minutes (1 hour = 60 minutes) 
Question 5.
  
 
Solution: 
Length of verandah (l) = 40m 
Breadth (b) = 15m 
Area = l x b = 40 x 15 = 600m² 
Length of one stone = 6dm =6/10 m 
and breadth = 5 dm =5/10 m 
Page 4


Question 1.
RS Aggarwal Solutions Class 7 Chapter 20 - Mensuration  (Ex 20A) Exercise 20A 
  
 
  
   
 
 
  
 
Solution:
 
 
(i) Length = 24.5 m 
Breadth = 18 m 
 ? Area of the rectangle = Length × 
Breadth 
= 24.5 m × 18 m 
 = 441 m
2 
 
 
(ii) Length = 12.5 m 
Breadth = 8 dm = (8 × 10) = 80 cm = 0.8 m     [since 1 dm = 10 cm and 1 
m = 100 cm] 
 ? Area of the rectangle = Length × Breadth 
= 12.5 m × 0.8 m 
= 10 m
2 
 
 
RS Aggarwal Solutions Class 7 Chapter 20 - Mensuration  (Ex 20A) Exercise 20A 
  
 
  
   
Solution:
 
Length of rectangular plot (l) = 48m
 
and its diagonal = 50m
 
 
Question 3.
 
 
Solution:
 
Ratio in the sides of a rectangle = 4 : 3
 
Area = 1728 cm²
 
Let length = 4x,
 
then breadth = 3x
 
Area = l x b
 
1728 = 4x x 3x
 
?
 
12x² = 1728
 
?
 
x² = 144 = (12)²
 
?
 
x = 12
 
Length = 4x = 4 x 12 = 48 m
 
and breadth = 3m = 3 x 12 = 36m
 
Question 2.
RS Aggarwal Solutions Class 7 Chapter 20 - Mensuration  (Ex 20A) Exercise 20A 
  
 
  
   
Now perimeter = 2 (l + b) = 2 (48 + 36) m = 2 x 84 = 168 m 
Rate of fencing = Rs. 30 per metre 
Total cost= 168 x 30 = Rs. 5040 
Question 4.
 
 
Solution: 
Area of rectangular field = 3584 m² 
Length = 64 m 
Area = 3584 
Breadth = Area / Length = 3584/64 = 56 m 
Now perimeter = 2 (l + b) = 2 (64 + 56) m = 2 x 120 = 240 m 
Distance covered in 5 rounds = 240 x 5 = 1200 m 
Speed = 6 km/h 
Time take = 1200/100 x 60/ 6  
= 12 minutes (1 hour = 60 minutes) 
Question 5.
  
 
Solution: 
Length of verandah (l) = 40m 
Breadth (b) = 15m 
Area = l x b = 40 x 15 = 600m² 
Length of one stone = 6dm =6/10 m 
and breadth = 5 dm =5/10 m 
RS Aggarwal Solutions Class 7 Chapter 20 - Mensuration  (Ex 20A) Exercise 20A 
  
 
  
   
Area of one stone = 6/10 x 5/10 
 
Question 6.
 
 
Solution:
 
Length of a room = 13 m
 
Breadth = 9 m
 
Area of floor = l x b = 13 x 9 m² = 117 m²
 
or area of carpet = 117 m²
 
Width = 75 cm 
 
=75/100 =3/4
 
m
 
Length of carpet = Area ÷ Width
 
= 117 ÷ 3/4
 
= 117 x 4/3m
 
= 39 x 4 = 156 m
 
Rate = Rs. 105 per m
 
Total cost = Rs. 156 x 105 = Rs. 16380
 
 
 
Page 5


Question 1.
RS Aggarwal Solutions Class 7 Chapter 20 - Mensuration  (Ex 20A) Exercise 20A 
  
 
  
   
 
 
  
 
Solution:
 
 
(i) Length = 24.5 m 
Breadth = 18 m 
 ? Area of the rectangle = Length × 
Breadth 
= 24.5 m × 18 m 
 = 441 m
2 
 
 
(ii) Length = 12.5 m 
Breadth = 8 dm = (8 × 10) = 80 cm = 0.8 m     [since 1 dm = 10 cm and 1 
m = 100 cm] 
 ? Area of the rectangle = Length × Breadth 
= 12.5 m × 0.8 m 
= 10 m
2 
 
 
RS Aggarwal Solutions Class 7 Chapter 20 - Mensuration  (Ex 20A) Exercise 20A 
  
 
  
   
Solution:
 
Length of rectangular plot (l) = 48m
 
and its diagonal = 50m
 
 
Question 3.
 
 
Solution:
 
Ratio in the sides of a rectangle = 4 : 3
 
Area = 1728 cm²
 
Let length = 4x,
 
then breadth = 3x
 
Area = l x b
 
1728 = 4x x 3x
 
?
 
12x² = 1728
 
?
 
x² = 144 = (12)²
 
?
 
x = 12
 
Length = 4x = 4 x 12 = 48 m
 
and breadth = 3m = 3 x 12 = 36m
 
Question 2.
RS Aggarwal Solutions Class 7 Chapter 20 - Mensuration  (Ex 20A) Exercise 20A 
  
 
  
   
Now perimeter = 2 (l + b) = 2 (48 + 36) m = 2 x 84 = 168 m 
Rate of fencing = Rs. 30 per metre 
Total cost= 168 x 30 = Rs. 5040 
Question 4.
 
 
Solution: 
Area of rectangular field = 3584 m² 
Length = 64 m 
Area = 3584 
Breadth = Area / Length = 3584/64 = 56 m 
Now perimeter = 2 (l + b) = 2 (64 + 56) m = 2 x 120 = 240 m 
Distance covered in 5 rounds = 240 x 5 = 1200 m 
Speed = 6 km/h 
Time take = 1200/100 x 60/ 6  
= 12 minutes (1 hour = 60 minutes) 
Question 5.
  
 
Solution: 
Length of verandah (l) = 40m 
Breadth (b) = 15m 
Area = l x b = 40 x 15 = 600m² 
Length of one stone = 6dm =6/10 m 
and breadth = 5 dm =5/10 m 
RS Aggarwal Solutions Class 7 Chapter 20 - Mensuration  (Ex 20A) Exercise 20A 
  
 
  
   
Area of one stone = 6/10 x 5/10 
 
Question 6.
 
 
Solution:
 
Length of a room = 13 m
 
Breadth = 9 m
 
Area of floor = l x b = 13 x 9 m² = 117 m²
 
or area of carpet = 117 m²
 
Width = 75 cm 
 
=75/100 =3/4
 
m
 
Length of carpet = Area ÷ Width
 
= 117 ÷ 3/4
 
= 117 x 4/3m
 
= 39 x 4 = 156 m
 
Rate = Rs. 105 per m
 
Total cost = Rs. 156 x 105 = Rs. 16380
 
 
 
RS Aggarwal Solutions Class 7 Chapter 20 - Mensuration  (Ex 20A) Exercise 20A 
  
 
  
   
Solution: 
Cost of carpeting a room = Rs. 19200 
Rate = Rs. 80 per m 
Length of carpet = 19200/80 m = 240 m 
Width of carpet = 75 cm =75/100 =3/4 m 
Area of carpet = 240 x 3/4= 180 m² 
Length of a room = 15 m 
Width =180/15 = 12m 
Question 8.
 
 
Solution: 
Ratio in length and breadth of a rectangular piece of land = 5 : 3 
Cost of fencing = Rs. 9600 
and rate = Rs. 24 per m 
Perimeter = 9600/24 = 400 m 
Let length = 5x 
Then breadth = 3x 
Perimeter = 2 (l + b) 
? 400 = 2 (5x + 3x) 
? 400 = 2 x 8x = 16x 
? 16x = 400 
? x = 25 
Length of the land = 5x = 5 x 25 = 125 m 
and width = 3x = 3 x 25 = 75 m 
Question 9. 
 
Solution:
 
Length of hall (l) = 10m.
 
Question 7.