Question

1. determine if the following side lengths form a right triangle: 4, 4, 4. explain your work.

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\) (where \(c\) is the hypotenuse, the longest side). Here, all sides are 4, so let \(a = 4\), \(b = 4\), \(c = 4\).

Step2: Calculate \(a^2 + b^2\) and \(c^2\)

\(a^2 + b^2 = 4^2 + 4^2 = 16 + 16 = 32\)
\(c^2 = 4^2 = 16\)

Step3: Compare results

Since \(32
eq 16\), \(a^2 + b^2
eq c^2\). Also, a right triangle must have one right angle (90°), but an equilateral triangle (all sides 4) has all angles 60°, so it's not a right triangle.

Answer:

The side lengths 4, 4, 4 do not form a right triangle.