Class 9 Maths Chapter 10 Assertion and Reason Questions - Heron’s Formula

Q1: Assertion: The area of a triangle is 8966.56 square cm, with sides measuring 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: (b)
The given assertion about the area of the triangle and its sides is correct. However, the reason provided is correct but not the direct explanation for the assertion. Heron's formula calculates the area of a triangle using its sides and the semi-perimeter, but it doesn't directly explain the given assertion.

Q2: Assertion: The area of an equilateral triangle with a side of 4 cm is 4√3 cm².
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 the assertion and reason are correct. The reason explains the formula for calculating the area of an equilateral triangle, which matches the given area in the assertion.

Q3: Assertion: Perimeter of a triangle = (a+b+c)/2
Reason: If the sides of the triangle are 30m, 24m, and 22m, then its perimeter is 76m.
(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: (b)
The assertion is about the formula for the perimeter of a triangle, which is correct. However, the reason provided does not directly explain the formula, but rather gives an example calculation.

Q4: Assertion: The side of an equilateral triangle is 6 cm, then the area of the triangle is 9√3 cm².
Reason: All the sides of an 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 the assertion and reason are correct. The reason directly explains the relationship between the side length and the area of an equilateral triangle.

Q5: Assertion: The height of an equilateral triangle is √3/2 times its side length (a).
Reason: If the side of an equilateral triangle is 6 cm, then the height 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)
The assertion is correct, and the reason provided is incorrect. The height of an equilateral triangle is indeed √3/2 times its side length, but the height for a side length of 6 cm is not 9 cm.

Q6: Assertion: The area of a triangle is 6 cm² with sides measuring 3 cm, 4 cm, and 5 cm.
Reason: Area of a 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)
The assertion and reason provided are both correct. The reason explains how the area of the triangle is calculated using Heron's formula, which involves the semi-perimeter and the lengths of the sides.

Q7: Assertion: Area of a 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 the assertion and reason are correct. The reason is a direct explanation of the assertion, where 's' represents the semi-perimeter of the triangle.

Q8: Assertion: If 2S = (a+b+c)/2 and the sides of a triangle are 3cm, 4cm, and 5cm, then the area = √s(s-a)(s-b)(s-c).
Reason: The area of a triangle with sides 3cm, 4cm, and 5cm is 6cm².
(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)
The assertion is correct and can be derived from Heron's formula. However, the reason is incorrect as it provides the area value for a specific triangle, which doesn't match the given sides.

Q9: Assertion: In a right-angled triangle, if the hypotenuse is 5√2 cm, then the other two sides are equal to 5 cm each.
Reason: In a right-angled triangle, base² + perpendicular² = hypotenuse².
(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 the assertion and reason are correct. The reason is a direct application of the Pythagorean theorem for a right-angled triangle.

Q10: Assertion: The height of a triangle is 18 cm, its area is 72 cm², and its base is 8 cm.
Reason: Area of a 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 the assertion and reason are correct. The reason provides the formula for calculating the area of a triangle using its base and height.