Question

Two sides of a triangle are 10 mm and 7 mm. Using the Triangle Inequality Theorem (see picture above), determine the length of the third side from the choices given.

(1 point)
O 3 mm
• 5 mm
O 1 mm
O 2 mm

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the possible range of the length of the third side, we need to apply the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let x be the length of the third side.

Therefore, we have:
10 + 7 > x
17 > x

Since x has to be less than the sum of the two given sides, we also have:
10 + x > 7
10 < x + 7
3 < x

Putting both inequalities together, we get:
3 < x < 17

Therefore, the length of the third side should be between 3 mm and 17 mm.

Given the choices, the closest option within this range is 5 mm. So, the length of the third side is 5 mm.