Chapter 12 Heron’s Formula Assertation & Reasoning Questions Class 9th Mathematics

1) Assertion: the area of a triangle 8966.56 whose sides are respectively 150 cm, 120 cm and 200 cm.

Reason: heron’s formula=√s(s-a)(s-b)(s-c)

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false.

d) both Assertion and reason are false.

Ans: a) both Assertion and reason are correct and reason is not correct explanation for Assertion

2) Assertion: the area of a triangle is 6 cm^2  whose sides are 3 cm, 4 cm and 5 cm respectively.

Reason: area of triangle= √s(s-a)(s-b)(s-c)

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false.

d) both Assertion and reason are false.

Ans:a) both Assertion and reason are correct and reason is correct explanation for Assertion

3) Assertion: the area of an equilateral triangle having each side 4 cm is 4√3 cm^2

Reason: Area of an equilateral triangle = ( √3/4 ) × a²

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false.

d) both Assertion and reason are false.

Ans:a) both Assertion and reason are correct and reason is correct explanation for Assertion

4) Assertion: area of triangle= √s(s-a)(s-b)(s-c)

Reason: s = (a+b+c)/2

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false.

d) both Assertion and reason are false.

Ans:a) both Assertion and reason are correct and reason is correct explanation for Assertion

5) Assertion: perimeter of triangle = (a+b+c)/2

Reason: If the sides of the triangle are 30m, 24m and 22 m then it’s perimeter is 76 m

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false.

d) both Assertion and reason are false.

Ans:a) both Assertion and reason are correct and reason is correct explanation for Assertion

6) Assertion: if 2S=( a+b+c)/2 where a,b,c are the sides of triangle then area =√s(s-a)(s-b)(s-c)

Reason: the sides of triangle are 3cm,4cm,5cm it’s area is 6cm^2

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false.

d) both Assertion and reason are false.

Ans:c)Assertion is true but reason is false

7) Assertion: the side of equilateral triangle is 6 cm then the area of triangle is  9 √3 cm^2

Reason: all the side of equilateral triangle are equal

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false.

d) both Assertion and reason are false.

Ans: a) both Assertion and reason are correct and reason is correct explanation for assertion.

8) Assertion: The right angled triangle if hypotenus is 5√2cm then  other two side equal to 5 cm each

Reason: in right angled triangle  base^2+perpendicular ^2=hypotenus ^2

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false.

d) both Assertion and reason are false.

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

9) Assertion: the height of equilateral triangle is √ 3/2a

Reason: the side of equilateral triangle  is 6 cm then the height of triangle is 9 cm

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false.

d) both Assertion and reason are false.

Ans: c) Assertion is true but reason is false.

10) Assertion: the height the triangle is 18 cm and its area is 72cm^2 and it’s base is 8 cm

Reason: area of triangle= 1/2*base*height

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false.

d) both Assertion and reason are false.

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

11) Assertion:  The sides of a triangle are 3 cm, 4 cm and 5 cm. Its area is 9√3cm^2

Reason : If 2s = (a + b + c ) , where a , b, c are the sides of a triangle, then area = √(s – a) (s–b)(s– c)

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false.

d) both Assertion and reason are false.

Ans: c) Assertion is true but reason is false

12)  Assertion : The sides of a triangle are in the ratio of 25 :14 :12 and its perimeter is 510 m. Then the greatest side is 250 cm.

Reason : Perimeter of a triangle = a + b + c , where a,b,c are sides of a triangle.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false.

d) both Assertion and reason are false.

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

13 )Assertion: Semi perimeter of a equilateral  triangle is s =3 a /2, where, a, are side of triangle.

Reason: If the area of an equilateral triangle is81√3 cm2, then the semi perimeter of triangle is 20cm.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false.

d) both Assertion and reason are false.

Ans: c) Assertion is correct but reason is false

14) Assertion: The sides of a triangle are in the atio of25 : 14 : 12 and its perimeter is 510 cm. Then the area of the triangle is 4449.08 cm2

Reason: Perimeter of a triangle = a + b + c, where a ,b, c are sides of a triangle.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false.

d) both Assertion and reason are false.

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

15) Assertion: the side of an equilateral triangle is 20cm then the height  is 20√3/3 cm

Reason: the height of an equilateral triangle is √3/2a

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false.

d) both Assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

16) Assertion: the perimeter of triangle is 36 cm and it’s side are in the ratio a:b:c= 3: 4:5 then a= 9 cm,b=12cm,c=15cm

Reason: perimeter of triangle = sum of all side of triangle

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false.

d) both Assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

17) Assertion: Area of rhombus whose side is 20 cm and one diagonal is 24 cmis 384cm^2

Reason: all sides of rhombus are equal

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false.

d) both Assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion