Question

if triangle ABC has sides of lengths 6, 10, and x + 3, between which two numbers must the value of x lie? a. 4 and 7. b.3 and 18. c. 1 and 13. d. 4 and 16

Answer 1

c. 1 and 13

Step-by-step explanation:

If we know two sides of a triangle, a and b, the third side c must be between a + b and a - b, so:

a - b < c < a + b

Therefore, the side withe length x + 3 can be between the following values:

10 - 6 < x + 3 < 10 + 6

4 < x + 3 < 16

Then, we can solve for x, so:

4 - 3 < x + 3 - 3 < 16 - 3

1 < x < 13

So, x is a number between 1 and 13.