Compare the square of the largest side length to the sum of the squares of the other two side lengths.
Acute
Practice makes perfect
We want to determine whether the triangle formed by the given side lengths is acute, right, or obtuse. To do so, we will compare the square of the largest side length to the sum of the squares of the other two side lengths. Let a, b, and c be the lengths of the sides, with c being the longest.
Condition
Type of Triangle
a^2+b^2 < c^2
Obtuse triangle
a^2+b^2 = c^2
Right triangle
a^2+b^2 > c^2
Acute triangle
Let's now consider the given side lengths 9cm, 10cm, and 12cm. Since 12 is the greatest of the numbers, we will let c be 12. We will also arbitrarily let a be 9 and b be 10.
9^2+10^2 ? 12^2
Let's simplify the above statement to determine whether the left-hand side is less than, equal to, or greater than the right-hand side.
