Question

1. which of the triangles below is not a right triangle?

6 ft, 8 ft, 12 ft
3 cm, 4 cm, 5 cm
\sqrt{6}in, \sqrt{10}in, \sqrt{4}in
27 cm, 36 cm, 45 cm

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\) (where \(c\) is the longest side).

Step2: Check 6 ft, 8 ft, 12 ft

Calculate \(6^2 + 8^2 = 36 + 64 = 100\), \(12^2 = 144\). Since \(100
eq144\), check other options.

Step3: Check 3 cm, 4 cm, 5 cm

\(3^2 + 4^2 = 9 + 16 = 25\), \(5^2 = 25\). So it is a right triangle.

Step4: Check \(\sqrt{6}\) in, \(\sqrt{10}\) in, \(\sqrt{4}\) in

\((\sqrt{4})^2 + (\sqrt{6})^2 = 4 + 6 = 10\), \((\sqrt{10})^2 = 10\). So it is a right triangle.

Step5: Check 27 cm, 36 cm, 45 cm

\(27^2 + 36^2 = 729 + 1296 = 2025\), \(45^2 = 2025\). So it is a right triangle.

Answer:

A. 6 ft, 8 ft, 12 ft