If a, b, c are the lengths of three sides of a triangle, then area of a triangle = √s(s - a)(s - b)(s - c), where s = perimeter of triangle. Is the given statement true or false and justify your answer.
Solution:
Given, a, b, c are the lengths of three sides of a triangle
Area of triangle = √s(s - a)(s - b)(s - c)
s = perimeter of triangle
We have to determine if the given statement is true or false.
By Heron’s formula,
Area of triangle = √s(s - a)(s - b)(s - c)
Where s= semiperimeter
s = (a + b + c)/2
Therefore, the given statement is false.
✦ Try This: If a, b, c are the lengths of three sides of a triangle, then area of a triangle = √s(s + a)(s + b)(s + c), where s = perimeter of triangle. Write True or False and justify your answer.
Given, a, b, c are the lengths of three sides of a triangle
Area of triangle = √s(s + a)(s + b)(s + c)
s = perimeter of triangle
We have to determine if the given statement is true or false.
By Heron’s formula,
Area of triangle = √s(s - a)(s - b)(s - c)
Where s= semiperimeter
s = (a + b + c)/2
Therefore, the given statement is false.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 12
NCERT Exemplar Class 9 Maths Exercise 12.2 Sample Problem 1
If a, b, c are the lengths of three sides of a triangle, then area of a triangle = √s(s - a)(s - b)(s - c), where s = perimeter of triangle. Is the given statement true or false and justify your answer.
Summary:
The given statement “If a, b, c are the lengths of three sides of a triangle, then area of a triangle = √s(s-a)(s-b)(s-c), where s = perimeter of triangle” is false
☛ Related Questions:
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