Question

1. is the triangle a right triangle? explain.

(image of a triangle with sides 6 cm, 8 cm, and hypotenuse 10 cm)

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse (longest side), and \(a,b\) are the legs.
Here, \(a = 6\), \(b = 8\), \(c = 10\).

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

\(6^2 + 8^2 = 36 + 64 = 100\)

Step3: Calculate \(c^2\)

\(10^2 = 100\)

Step4: Compare results

Since \(6^2 + 8^2 = 10^2\), the triangle satisfies the Pythagorean theorem.

Answer:

Yes, the triangle is a right triangle. Because for the side lengths 6 cm, 8 cm, and 10 cm, \(6^2 + 8^2 = 36 + 64 = 100\) and \(10^2 = 100\), so it satisfies the Pythagorean theorem \(a^2 + b^2 = c^2\) (where \(a = 6\), \(b = 8\), \(c = 10\)), indicating it is a right triangle.