Question

Two sides of a triangle measure 15 inches and 18 inches, respectively. which of these is not a possible length for the third side of the triangle?
a.4 inches
b.18 inches
c.24 inches
d.36 inches

Answer 1

Answer:

Option d. 36 inches

Step-by-step explanation:

As we know in a triangle if the measurement of two sides are given then third side of the triangle should be less than the sum of these two sides. Otherwise construction of a triangle is not possible.

Here two sides are 15 inches and 18 inches so third side of the triangle should be less than 18+15 = 33.

Third side < 33

Therefore third side with the measurement of 36 inches is not possible.

Option d. 36 inches is the answer.

Answer 2

The sum of the lengths of the two sides given is 15 inches + 18 inches = 33 inches. The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This means that the length of the third side of the triangle must be less than 33 inches. It also means that the length of the third side of the triangle must be greater than the difference between the lengths of the two sides given, which is 18 inches – 15 inches = 3 inches. Since the third side must have a length of between 3 inches and 33 inches, the third side of the triangle cannot have a length of 36 inches.