Question

1. landon welded three pieces of metal together to form a triangle with side lengths that measure 8 inches, 9 inches and 17 inches. is the triangle that landon created a right triangle? explain.

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, the sum of the squares of the two shorter sides (legs) should equal the square of the longest side (hypotenuse). The formula is \(a^2 + b^2 = c^2\), where \(c\) is the longest side, and \(a\) and \(b\) are the other two sides.
Here, \(a = 8\), \(b = 9\), and \(c = 17\).

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

\(a^2 = 8^2 = 64\)
\(b^2 = 9^2 = 81\)
So, \(a^2 + b^2 = 64 + 81 = 145\)

Step3: Calculate \(c^2\)

\(c^2 = 17^2 = 289\)

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

Since \(145
eq 289\), the Pythagorean theorem is not satisfied.

Answer:

No, the triangle is not a right triangle because \(8^2 + 9^2 = 145\) and \(17^2 = 289\), and \(145
eq 289\), so the Pythagorean theorem does not hold.