Question

warm up #10
can the following form a triangle?
if so, is it a right, obtuse, or acute?
3 feet, 4 feet, and 6 feet

Explanation:

Step1: Check Triangle Inequality

To form a triangle, the sum of any two sides must be greater than the third side.

• \(3 + 4 = 7 > 6\)
• \(3 + 6 = 9 > 4\)
• \(4 + 6 = 10 > 3\)

So, it can form a triangle.

Step2: Classify by Pythagorean Theorem

Let \(a = 3\), \(b = 4\), \(c = 6\) (longest side).
Check \(a^2 + b^2\) vs \(c^2\):
\(a^2 + b^2 = 3^2 + 4^2 = 9 + 16 = 25\)
\(c^2 = 6^2 = 36\)
Since \(a^2 + b^2 < c^2\) (\(25 < 36\)), the triangle is obtuse.

Answer:

Yes, it can form a triangle, and it is an obtuse triangle.