I know it is a long question but please I will mark brainlist to the person who answers please help

Carla lives 16 miles from the Library.

The mistake is drawng the diagram incorrectly and using the miles given in the wrong places. The student's diagram has Yuri in a place that's Southwest of the Library in the diagram given

Step-by-step explanation:

If Yuri lives 24 miles SOUTH of the library, the "b" side of the triangle should be 24, with the Library at the top and Yuri at the bottom left, which is the west end of the base. The base "a" of the triangle should extend 10 to the right (East in compas directions) forming the right angle. Carla lives at the sharp southeast corner of the triangle, and the Hypotenuse "c"  from her house to the Library is the distance we have to figure.

c² =a² + b²

c² = 10² + 24²

c² = 100 + 576

c² = 676

√c² = √676

c = 26       Carla lives 26 miles from the Library.

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.