Question

(SAT Prep) If two sides of a triangle are 2 and 4, the third side may be:

Answer 1

Answer:

C

Step-by-step explanation:

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side. Note: This rule must be satisfied for all 3 conditions of the sides

Try A (2,4,7)

2+4<7 so it is wrong

Try B (2,4,2)

2+4>2

2+2 = 4 wrong

Try D (2,4,6)

2+4 = 6 wrong

Try C (2,4,5)

2+4>5

4+5>2

5+2>4

yay it works

Answer 2

Answer: (C) 5

Step-by-step explanation:

The triangle inequality states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. Therefore, if x is the third side, then 2+4>x, and x+2>4.

Therefore, x<6 and x>2, meaning that 2<x<6. The only choice that satisfies this is 5.