Question

question 4 of 50
if the side lengths of a triangle are 3, 6, and 7, then the triangle is obtuse.
true
false

Explanation:

Step1: Recall triangle type rule

For a triangle with sides \(a \leq b \leq c\), check \(a^2 + b^2\) vs \(c^2\). If \(a^2 + b^2 < c^2\), obtuse; \(=\) right; \(>\) acute.

Step2: Identify sides

Here, \(a = 3\), \(b = 6\), \(c = 7\).

Step3: Calculate squares

\(a^2 = 3^2 = 9\), \(b^2 = 6^2 = 36\), \(c^2 = 7^2 = 49\).

Step4: Compare \(a^2 + b^2\) and \(c^2\)

\(a^2 + b^2 = 9 + 36 = 45\). Since \(45 < 49\) (\(a^2 + b^2 < c^2\)), triangle is obtuse.

Answer:

True