Calculation of DE in Triangle ABC

Given information:

• Triangle ABC
• Side AB = 24 cm
• Side AC = 24 cm
• AD = 3/8 AC
• AE = 3/8 AB

To find:

• DE

Solution:

1. Calculate the lengths of AD and AE:
   • AD = (3/8) * AC
   • AD = (3/8) * 24 cm
   • AD = 9 cm
   • AE = (3/8) * AB
   • AE = (3/8) * 24 cm
   • AE = 9 cm
2. Use the triangle inequality theorem to determine the relationship between the lengths of the sides of a triangle:
   • In any triangle, the sum of the lengths of any two sides is always greater than the length of the third side.
3. Apply the triangle inequality theorem to triangle ADE:
   • AD + AE > DE
   • 9 cm + 9 cm > DE
   • 18 cm > DE
4. Therefore, DE must be less than 18 cm.

Conclusion:

• The length of DE in triangle ABC is less than 18 cm.