Question

Iliana claims that she can construct a triangle from a 12-inch rod, a 36-inch rod, and a 39.4-inch rod. Which statement explains whether she is correct?

A) Iliana cannot construct a triangle because the sum of the two smaller sides will not be greater than the third side.

B) Iliana cannot construct a triangle because the ruler is not long enough to connect the longer sticks.
C) Iliana will be able to construct a triangle because the sum of any two sides is greater than the third side.
D) Iliana will be able to construct a triangle because the sum of any two sides is less than the third side.

Answer 1

C is the answer

Explanation:

Answer 2

The answer is C) Iliana will be able to construct a triangle because the sum of any two sides is greater than the third side.

In the triangle, the sum of any two sides is always greater than the third side.
Let's just check out Iliana's triangle:
a = 12 in
b = 36 in
c = 39.4 in

a + b > c
12 + 36 > 39.4
48 > 39.4

a + c > b
12 + 39.4 > 36
51.4 > 36

b + c > a
36 + 39.4 > 12
75.4 > 12

Since we showed that the sum of any two sides is always greater than the third side, Iliana's statement is correct.