Question

ACT geometry help?

A certain triangle has sides each with integer lengths. if two of the sides are 4 units long and 7 units long, what is the greatest possible value, in units, for the triangle's perimeter?
f) 7
g) 10
h) 12
j) 21
k) 22

Answer 1

Third side should be more than 7-4=3, but less than 7+4=11.

So 3d greatest side will be 10, because it should be integer, but it cannot be 11.

The greatest perimeter = 4+7+10=21.

Answer: j.21.