Do the given numbers satisfy the Triangle Inequality Theorem. If so, compare the square of the largest side to the sum of the squares of the other two sides.
Is it a triangle: Yes Type of triangle: Acute
Practice makes perfect
First, we want to know if the numbers 10, 16, 18 can be the three sides of a triangle. If yes, they have to fulfill the Triangle Inequality Theorem. This theorem tells us that the sum of a triangle's smaller sides must be greater than its longest side.
10+16? >18 ⇔ 26 >18 ✓
As we can see, the sides can form a triangle. Next, we want to determine if the triangle is obtuse, right or acute. The following three conditions applies. Notice that c is the longest side in each of the conditions.
Condition
Type of Triangle
a^2+b^2 < c^2
Obtuse
a^2+b^2 = c^2
Right
a^2+b^2 > c^2
Acute
We want to know if the left-hand side is less than, equal to, or greater than the right-hand side.
