Question

Could 8.8 cm, 8.0 cm and 8.8 cm be the side lengths of a triangle?

Choose 1 answer:


(Choice A)


Yes


(Choice B)


No

Answer 1

yes it is possible to have a triangle with 8.8 cm, 8.0 cm and 8.8 cm.

Explanation:

Condition on sides of triangle:

• The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
• It is not possible to have sum to be less than the length of the third side.
• A triangle with three given positive side lengths exists if and only if those side lengths satisfy the given condition
• Let a, b and c be three sides of triangle.

`a + b > c\\a+c>b\\b+c>a`

Here, we are given that a = 8.8 cm, b = 8.0 cm, c = 8.8 cm

We check for the triangular inequality:

`1.~8.8 + 8.0 > 8.8\\16.8>8.8\\2.~8.8+8.8>8.0\\17.6>8.0\\3.~8.0+8.8>8.8\\16.8>8.8`

Thus, yes it is possible to have a triangle with given measurements.