Tell if the measures 18, 20 and 27 can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse or right. Please explain.

In a triangle the sum of any two sides of the triangles is
greater than the third side. A triangle can be formed by any set of three lines that satisfy this
condition.

As we see below this condition is satisfied for the set
of given lines that have length of 18, 20 and 27.

18 + 20 >
27

20 + 27 > 18

18 + 27 >
20

In an triangle the biggest angle is formed by the two smallest
sides. We can find if this angle is equal to, less than, or more than right angle as
follows.

Let the two smaller sides be equal to a and be and the
biggest side be c. Then the angle formed by a and b
is:

• Right angle if a^2 + b^2 =
  c^2

• Obtuse angle if a^2 + b^2 <
  c^2

• Acute angle if a^2 + b^2 >
  c^2

For the given three
lines:

a^2 + b^2 = 18^2 + 20^2 =
724

c^2 = 27^2 = 729

Thus we see that
a^2 + b^2 < c^2. Therefore the angle is an obtuse angle, and the triangle formed by the
lines is an obtuse triangle.