Question

Determine the length of the third side of a triangle from the choices provided if the first two sides measure 10 and 12.(1 point)
Responses

22
22

15
15

24
24

30

Pls be right bot

Answer 1

To determine the possible length of the third side of a triangle when the first two sides measure 10 and 12, we can use the triangle inequality theorem. This theorem states that for any triangle with sides of lengths \( a \), \( b \), and \( c \):

1. \( a + b > c \)
2. \( a + c > b \)
3. \( b + c > a \)

Let the lengths of the two sides be \( a = 10 \) and \( b = 12 \). Let \( c \) be the length of the third side.

Using the triangle inequalities:

1. \( 10 + 12 > c \) ⇒ \( c < 22 \)
2. \( 10 + c > 12 \) ⇒ \( c > 2 \)
3. \( 12 + c > 10 \) ⇒ \( c > -2 \) (this inequality is always true for positive \( c \))

From the first two inequalities, we find:
- \( 2 < c < 22 \)

Therefore, the length of the third side must be greater than 2 and less than 22. The only response you provided that falls within this range is **15**.

So, the length of the third side of the triangle is **15**.