Question

1. do these measurements form a right triangle?

side 1: 32
side 2: 21
side 3: 12

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, the Pythagorean theorem states that \(a^2 + b^2 = c^2\), where \(c\) is the longest side (hypotenuse), and \(a\), \(b\) are the other two sides. Here, the longest side is 32, so we check if \(21^2 + 12^2 = 32^2\).

Step2: Calculate \(21^2 + 12^2\)

\(21^2 = 441\), \(12^2 = 144\). Then \(21^2 + 12^2 = 441 + 144 = 585\).

Step3: Calculate \(32^2\)

\(32^2 = 1024\).

Step4: Compare results

Since \(585
eq 1024\), the equation \(a^2 + b^2 = c^2\) does not hold.

Answer:

No, these measurements do not form a right triangle.