Question

Which of the following sets of numbers could be the lengths of the sides of a triangle? A. 81 mm, 7 mm, 6 mm B. 81 mm, 7 mm, 72 mm C. 81 mm, 7 mm, 88 mm D. 81 mm, 7 mm, 77 mm

Answer 1

We know that
The triangle inequality states that for any triangle, the sum of the lengths of any two sides of a triangle is greater than the length of the third side
so
case A. 81 mm, 7 mm, 6 mm 
6+7 is not > 81

case B. 81 mm, 7 mm, 72 mm
72+7 is not > 81

case C. 81 mm, 7 mm, 88 mm
81+7 is not > 88

case D. 81 mm, 7 mm, 77 mm
81+7 is > 77------> ok
77+7 is > 81-----> ok
81+77 is > 7-----> is ok

the answer is the option
D. 81 mm, 7 mm, 77 mm