Question

Which of the following set of measurements cannot be the lengths of sides of a triangle?

• A. $37\frac{1}{4}cm,18\frac{1}{2}cm,25\frac{3}{4}cm$
  
• B. $42\frac{1}{2}cm,73\frac{1}{4}cm,30\frac{1}{2}cm$
  
• C. $48\frac{3}{4}cm,59\frac{1}{2}cm,45\frac{1}{4}cm$
  
• D. $7\frac{1}{4}cm,8\frac{1}{2}cm,15cm$
  

Answer 1

The correct option is B $42\frac{1}{2}cm,73\frac{1}{4}cm,30\frac{1}{2}cm$


In a triangle, the sum of two sides is always greater than the third side.
Consider the lengths of sides of a triangle as $42\frac{1}{2}cm,73\frac{1}{4}\text{cm and 30}\frac{1}{2}cm$
Now, $42\frac{1}{2}+30\frac{1}{2}=73<\frac{1}{4}$
Since the sum is less than the third side, therefore, such a triangle cannot be constructed.
Hence, the correct answer is option (b).