Question

Triangle ABC has AB=4 and BC=7 then, (A) AC<7 (B) AC>4 (C) 4<AC<7 (D) 3<AC<11​​

Answer 1

Given

• Triangle ABC
• AB=4
• BC=7

To find

• the correct expression for the side AC

Solution

we are provided with a triangle and are given with the lengths of two sides and are asked to pick the correct expression for the third side.

we know that a triangle can only be drawn if the third side is less than the sum of the two sides and the third side can be less than the smallest side given

according to the first condition,

AB + BC > AC

Or, 7 + 4 > AC

Or, 11 > AC

according to the second condition,

AC > 3 (smallest side given is 4)

combining both of this we get,

3<AC<11

therefore the correct option is d