RD Sharma MCQs: Heron's Formula | Mathematics (Maths) Class 9 PDF Download

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Question:36
Mark the correct alternative in each of the following:
The sides of a triangle are 16 cm, 30 cm, 34 cm. Its area is
a
225 cm
2
b
240 cm
2
c
225v 2
cm
2
d
450 cm
2
Solution:
Page 2


  
                   
                  
       
    
                    
             
               
  
     
   
Question:36
Mark the correct alternative in each of the following:
The sides of a triangle are 16 cm, 30 cm, 34 cm. Its area is
a
225 cm
2
b
240 cm
2
c
225v 2
cm
2
d
450 cm
2
Solution:
The area of a triangle having sides a, b, c and s as semi-perimeter is given by,
, where
 
Therefore the area of a triangle say A, having sides 16 cm, 30 cm and 34 cm is given by
a = 16 cm ; b = 30 cm ; c = 34 cm
 
 
 
 
 
Therefore the area of the triangle is 
Hence, the correct option is b
.
Question:37
The base of an isosceles right triangle is 30 cm. Its area is
a
225 cm
2
b
225 v 3
cm
2
c
225 v 2
cm
2
d
450 cm
2
Solution:
Let ABC be the right triangle in which ?B = 90°. Now, base = BC; perpendicular = AB; Hypotenuse = ACNow, BC = 30 cm (given)Now, ? ABC is an isosceles right angled ? and we know
Hence, the correct option is d
.
Question:38
The sides of a triangle are 7 cm, 9 cm and 14 cm. Its area is
a
12v 5 cm
2
b
12v 3 cm
2
c
24v 5 cm
2
d
63 cm
2
Solution:
The area of a triangle having sides a, b, c and s as semi-perimeter is given by,
, where
Therefore the area of a triangle having sides 7 cm, 9 cm and 14 cm is given by
a = 7 cm ; b = 9 cm ; c = 14 cm
Page 3


  
                   
                  
       
    
                    
             
               
  
     
   
Question:36
Mark the correct alternative in each of the following:
The sides of a triangle are 16 cm, 30 cm, 34 cm. Its area is
a
225 cm
2
b
240 cm
2
c
225v 2
cm
2
d
450 cm
2
Solution:
The area of a triangle having sides a, b, c and s as semi-perimeter is given by,
, where
 
Therefore the area of a triangle say A, having sides 16 cm, 30 cm and 34 cm is given by
a = 16 cm ; b = 30 cm ; c = 34 cm
 
 
 
 
 
Therefore the area of the triangle is 
Hence, the correct option is b
.
Question:37
The base of an isosceles right triangle is 30 cm. Its area is
a
225 cm
2
b
225 v 3
cm
2
c
225 v 2
cm
2
d
450 cm
2
Solution:
Let ABC be the right triangle in which ?B = 90°. Now, base = BC; perpendicular = AB; Hypotenuse = ACNow, BC = 30 cm (given)Now, ? ABC is an isosceles right angled ? and we know
Hence, the correct option is d
.
Question:38
The sides of a triangle are 7 cm, 9 cm and 14 cm. Its area is
a
12v 5 cm
2
b
12v 3 cm
2
c
24v 5 cm
2
d
63 cm
2
Solution:
The area of a triangle having sides a, b, c and s as semi-perimeter is given by,
, where
Therefore the area of a triangle having sides 7 cm, 9 cm and 14 cm is given by
a = 7 cm ; b = 9 cm ; c = 14 cm
Therefore the answer is
a.
Question:39
The sides of a triangular field are 325 m, 300 m and 125 m. Its area is
a
18750 m
2
b
37500 m
2
c
97500 m
2
d
48750 m
2
Solution:
The area of a triangle having sides a, b, c and s as semi-perimeter is given by,
, where
 
Therefore the area of a triangular field, say A having sides 325 m, 300 m and 125 m is given by
a = 325 m ; b = 300 m ; c = 125 m
Therefore, the correct answer is
a.
Question:40
The sides of a triangle are 50 cm, 78 cm and 112 cm. The smallest altitude is
a
20 cm
b
30 cm
c
40 cm
d
50 cm
Solution:
The area of a triangle having sides a, b, c and s as semi-perimeter is given by,
, where
Therefore the area of a triangle, say A having sides 50 cm, 78 cm and 112 cm is given by
The area of a triangle, having p as the altitude will be,
Area = 
1
2
×base ×height
Where, A = 1680 
Page 4


  
                   
                  
       
    
                    
             
               
  
     
   
Question:36
Mark the correct alternative in each of the following:
The sides of a triangle are 16 cm, 30 cm, 34 cm. Its area is
a
225 cm
2
b
240 cm
2
c
225v 2
cm
2
d
450 cm
2
Solution:
The area of a triangle having sides a, b, c and s as semi-perimeter is given by,
, where
 
Therefore the area of a triangle say A, having sides 16 cm, 30 cm and 34 cm is given by
a = 16 cm ; b = 30 cm ; c = 34 cm
 
 
 
 
 
Therefore the area of the triangle is 
Hence, the correct option is b
.
Question:37
The base of an isosceles right triangle is 30 cm. Its area is
a
225 cm
2
b
225 v 3
cm
2
c
225 v 2
cm
2
d
450 cm
2
Solution:
Let ABC be the right triangle in which ?B = 90°. Now, base = BC; perpendicular = AB; Hypotenuse = ACNow, BC = 30 cm (given)Now, ? ABC is an isosceles right angled ? and we know
Hence, the correct option is d
.
Question:38
The sides of a triangle are 7 cm, 9 cm and 14 cm. Its area is
a
12v 5 cm
2
b
12v 3 cm
2
c
24v 5 cm
2
d
63 cm
2
Solution:
The area of a triangle having sides a, b, c and s as semi-perimeter is given by,
, where
Therefore the area of a triangle having sides 7 cm, 9 cm and 14 cm is given by
a = 7 cm ; b = 9 cm ; c = 14 cm
Therefore the answer is
a.
Question:39
The sides of a triangular field are 325 m, 300 m and 125 m. Its area is
a
18750 m
2
b
37500 m
2
c
97500 m
2
d
48750 m
2
Solution:
The area of a triangle having sides a, b, c and s as semi-perimeter is given by,
, where
 
Therefore the area of a triangular field, say A having sides 325 m, 300 m and 125 m is given by
a = 325 m ; b = 300 m ; c = 125 m
Therefore, the correct answer is
a.
Question:40
The sides of a triangle are 50 cm, 78 cm and 112 cm. The smallest altitude is
a
20 cm
b
30 cm
c
40 cm
d
50 cm
Solution:
The area of a triangle having sides a, b, c and s as semi-perimeter is given by,
, where
Therefore the area of a triangle, say A having sides 50 cm, 78 cm and 112 cm is given by
The area of a triangle, having p as the altitude will be,
Area = 
1
2
×base ×height
Where, A = 1680 
We have to find the smallest altitude, so will substitute the value of the base AC with the length of each side one by one and find the smallest altitude distance i.e. p
Case 1 
Case 2
Case 3
Therefore, the answer is
b.
Question:41
The sides of a triangle are 11 m, 60 m and 61 m. The altitude to the smallest side is
a
11 m
b
66 m
c
50 m
d
60 m
Solution:
The area of a triangle having sides a, b, c and s as semi-perimeter is given by,
, where
We need to find the altitude to the smallest side
 
Therefore the area of a triangle having sides 11 m, 60 m and 61 m is given by
a = 11 m ; b = 60 m ; c = 61 m
 
The area of a triangle having base AC and height p is given by
We have to find the height p corresponding to the smallest side of the triangle. Here smallest side is 11 m 
AC = 11 m
Therefore, the answer is
Page 5


  
                   
                  
       
    
                    
             
               
  
     
   
Question:36
Mark the correct alternative in each of the following:
The sides of a triangle are 16 cm, 30 cm, 34 cm. Its area is
a
225 cm
2
b
240 cm
2
c
225v 2
cm
2
d
450 cm
2
Solution:
The area of a triangle having sides a, b, c and s as semi-perimeter is given by,
, where
 
Therefore the area of a triangle say A, having sides 16 cm, 30 cm and 34 cm is given by
a = 16 cm ; b = 30 cm ; c = 34 cm
 
 
 
 
 
Therefore the area of the triangle is 
Hence, the correct option is b
.
Question:37
The base of an isosceles right triangle is 30 cm. Its area is
a
225 cm
2
b
225 v 3
cm
2
c
225 v 2
cm
2
d
450 cm
2
Solution:
Let ABC be the right triangle in which ?B = 90°. Now, base = BC; perpendicular = AB; Hypotenuse = ACNow, BC = 30 cm (given)Now, ? ABC is an isosceles right angled ? and we know
Hence, the correct option is d
.
Question:38
The sides of a triangle are 7 cm, 9 cm and 14 cm. Its area is
a
12v 5 cm
2
b
12v 3 cm
2
c
24v 5 cm
2
d
63 cm
2
Solution:
The area of a triangle having sides a, b, c and s as semi-perimeter is given by,
, where
Therefore the area of a triangle having sides 7 cm, 9 cm and 14 cm is given by
a = 7 cm ; b = 9 cm ; c = 14 cm
Therefore the answer is
a.
Question:39
The sides of a triangular field are 325 m, 300 m and 125 m. Its area is
a
18750 m
2
b
37500 m
2
c
97500 m
2
d
48750 m
2
Solution:
The area of a triangle having sides a, b, c and s as semi-perimeter is given by,
, where
 
Therefore the area of a triangular field, say A having sides 325 m, 300 m and 125 m is given by
a = 325 m ; b = 300 m ; c = 125 m
Therefore, the correct answer is
a.
Question:40
The sides of a triangle are 50 cm, 78 cm and 112 cm. The smallest altitude is
a
20 cm
b
30 cm
c
40 cm
d
50 cm
Solution:
The area of a triangle having sides a, b, c and s as semi-perimeter is given by,
, where
Therefore the area of a triangle, say A having sides 50 cm, 78 cm and 112 cm is given by
The area of a triangle, having p as the altitude will be,
Area = 
1
2
×base ×height
Where, A = 1680 
We have to find the smallest altitude, so will substitute the value of the base AC with the length of each side one by one and find the smallest altitude distance i.e. p
Case 1 
Case 2
Case 3
Therefore, the answer is
b.
Question:41
The sides of a triangle are 11 m, 60 m and 61 m. The altitude to the smallest side is
a
11 m
b
66 m
c
50 m
d
60 m
Solution:
The area of a triangle having sides a, b, c and s as semi-perimeter is given by,
, where
We need to find the altitude to the smallest side
 
Therefore the area of a triangle having sides 11 m, 60 m and 61 m is given by
a = 11 m ; b = 60 m ; c = 61 m
 
The area of a triangle having base AC and height p is given by
We have to find the height p corresponding to the smallest side of the triangle. Here smallest side is 11 m 
AC = 11 m
Therefore, the answer is
d.
Question:42
The sides of a triangle are 11 cm, 15 cm and 16 cm. The altitude to the largest side is
a
30v 7 cm
b
15
v
7
2
cm
c
15
v
7
4
cm
d
30 cm
Solution:
The area of a triangle having sides a, b, c and s as semi-perimeter is given by,
, where
We need to find the altitude corresponding to the longest side
 
Therefore the area of a triangle having sides 11 cm, 15 cm and 16 cm is given by
a = 11 m ; b = 15 cm ; c = 16 cm
 
The area of a triangle having base AC and height p is given by
We have to find the height p corresponding to the longest side of the triangle.Here longest side is 16 cm, that is AC=16 cm 
Therefore, the answer is
c.
Question:43
The base and hypotenuse of a right triangle are respectively 5 cm and 13 cm long. Its area is
a
25 cm
2
b
28 cm
2
c
30 cm
2
d
40 cm
2
Solution:
In right angled triangle ABC having base 5 cm and hypotenuse 13 cm we are asked to find its area
Using Pythagorean Theorem
Where, AB = hypotenuse = 13 cm, AC = Base = 5 cm, BC = Height