cash register

[nervesofsteel]

A cash register in a certain clothing store is the same distance from two dressing rooms in the store. If the distance between the two dressing rooms is 16 feet, which of the following could be the distance between the cash register and either dressing room?

I. 6 feet
II. 12 feet
III. 24 feet


A. I only
B. II only
C. III only
D. I and II
E. II and III

OAE

[ssmiles08]

If you make an isosceles triangle with d---d = 16 and the other two lines as x and x.

If 6 is x , the other length must at least be greater than 10 (16-6). Since we know the other length is also 6, and this is less than 10, this cannot be true.

12 works because the smallest length can be 4 and the biggest length can be (16+12) = 28. Since 12 falls into this category, 12 is a possible distance.

24 also works. 24-16 = 8 (smallest length) (24+16) = 40. We know x is 24, so 8 < 24 < 40.

Therfore it is (E)

[nervesofsteel]

If you make an isosceles triangle with d---d = 16 and the other two lines as x and x.

If 6 is x , the other length must at least be greater than 10 (16-6). Since we know the other length is also 6, and this is less than 10, this cannot be true.

12 works because the smallest length can be 4 and the biggest length can be (16+12) = 28. Since 12 falls into this category, 12 is a possible distance.

24 also works. 24-16 = 8 (smallest length) (24+16) = 40. We know x is 24, so 8 < 24 < 40.

Therfore it is (E)

Thanks i forgot didn't use the properties of triangle....

a+b > c