basically the cash register location alongwith the two dressing rooms with make an isosceles triangle

Property: For a triangle to exist Sum of the two shorter sides must be greater than the longest side

I. 6 feet --- i.e. 6+6 is NOT greater than 16 hence INCORRECT
II. 12 feet --- i.e. 12+12 is greater than 16 hence CORRECT
III. 24 feet --- i.e. 16+24 is greater than 24 hence CORRECT

Answer: option E
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We see that we have an isosceles triangle with its base equal to 16 feet. The other two sides must be equal. We can use the triangle inequality theorem to determine the possible lengths of those two equal sides. The theorem states that the sum of the lengths of the two shortest sides is greater than the length of the longest side.

I. 6 feet

The resulting triangle would have sides of 6, 6, and 16. The two other sides cannot be 6 since 6 + 6 is not greater than 16.

II. 12 feet

The resulting triangle would have sides of 12, 12, and 16. The two other sides can be 12 since 12 + 12 is greater than 16.

III. 24 feet

The resulting triangle would have sides of 24, 24, and 16. The two other sides can be 24 feet since 16 + 24 is greater than 24. (Note in this case that the two shortest sides are 16 and 24.)

Answer: E
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can we also find out the range of the 2 sides and see if they fall between the sides.

Why can't the placement be in a straight line? Is there something in the statement that makes it a triangle?

How can both dressing rooms be of equal distance from register if they are in vertical line?

the second dressing room in line will be much farther than the original one.

Could this also be solved using the Triangle property of : The length of any side of a triangle MUST BE LARGER than the positive difference of the other 2 sides, but SMALLER than the sum of the other 2 sides?

I ) 6-6<16< 6+6 => 0<16<12 (NOT POSSIBLE)
II) 12-12 <16<12+12 => 0<16<24 (POSSIBLE)
III) 24-24 < 16 < 24+24 => 0<16>48 (POSSIBLE)

Is my understanding of this property correct?

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