# 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:**

- The area of a triangle with base 4 cm and height 6 cm is 24 cm². Is the given statement true or fals . . . .
- The area of ∆ ABC is 8 cm² in which AB = AC = 4 cm and ∠A = 90º. Is the given statement true or fals . . . .
- The area of the isosceles triangle is 5/4 √11 cm² , if the perimeter is 11 cm and the base is 5 cm. . . . .

visual curriculum