Home > Geometry > Triangle Inequality Theorem

If three sides are given as follows, in which case / cases is it possible to draw a triangle?

A) 6 cm, 8 cm, and 16 cm
B) 6 cm, 8 cm, and 10 cm
C) 6 cm, 7 cm, and 14 cm
D) 6 cm, 7 cm, and 20 cm

Answer 1

Caroline Aucoin

I think B)

I tried to build a right triangle by using Pythagora's theorem:

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Answer 2

Aaliyah Anderson

Answer is B

To form a triangle using three given lengths,

one should check that

the sum of smaller two sides is greater than the largest side.

Among te given cases

A) 6 cm, 8 cm, and 16 cm

B) 6 cm, 8 cm, and 10 cm

C) 6 cm, 7 cm, and 14 cm

D) 6 cm, 7 cm, and 20 cm

this is so only in case B.

Hence, we can form a triangle only with sides given at B.

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Answer 3

Allison Allen

A triangle can be drawn if and only if the sum of the lengths of any two sides is greater than the length of the third side. This condition is known as the triangle inequality theorem. Therefore, given three side lengths (a), (b), and (c), a triangle can be drawn if:

(a + b > c)
(a + c > b)
(b + c > a)

If any of these conditions are not met, then it is not possible to draw a triangle with the given side lengths.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.