Q. 18

# If a, b, and c are the sides of a triangle such that a + b = c. Prove that the area of a triangle equals to zero. Find the value for which area is not equal to zero.

To Find: Value for which area is not equal to zero.

Given: a, b, and c are sides of the triangle and a + b = c.

Concept Used:

If sides of a triangle are a, b, and c, then area of a triangle is given by:

Where s = semiperimeter of the triangle

Explanation:

Putting, a + b = c

Area = 0

Hence, with the given condition, Area = 0.

Now, we know that the square root does not contain a negative value.

Therefore,

(a + b) > c will give positive values.

Hence, for (a + b) > c, area of the triangle is not equal to zero.

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