Question

The lengths of two sides of a triangle are 20 cm and 32 cm.

Explain why the third side of the triangle can or cannot have a length of 10 cm

Answer 1

No

Explanation:

By the Triangle Inequality Theorem, for sides a, b, and c of a triangle:

a + b > c

a + c > b

b + c > a

Here, we already have two sides of lengths 20 and 32. We want to see if the third side can be 10 cm. Suppose a = 32, b = 20, and c = 10. According to the Triangle Inequality Theorem:

20 + 32 >? 10 ⇒ 52 > 10 ----- that's good

32 + 10 >? 20 ⇒ 42 > 20 ----- that's also good

20 + 10 >? 32 ⇒ 30 > 32 ----- this is false

So, the third side cannot be 10 because that would violate the theorem.

Hope this helps!