Question

1. choose the correct answer.

a = 28 mm, b = 45 mm, c = 53 mm
the triangle is a(n) ____ triangle.
right
acute
obtuse

Explanation:

Step1: Recall Pythagorean theorem

For a triangle with sides \(a\), \(b\), \(c\) (where \(c\) is the longest side), check if \(a^2 + b^2 = c^2\) (right), \(a^2 + b^2>c^2\) (acute), or \(a^2 + b^2 < c^2\) (obtuse).
Calculate \(a^2 + b^2\): \(28^2+45^2 = 784 + 2025=2809\).

Step2: Calculate \(c^2\)

\(c = 53\), so \(c^2=53^2 = 2809\).

Step3: Compare results

Since \(a^2 + b^2=c^2\) (2809 = 2809), by Pythagorean theorem, the triangle is right.

Answer:

A. right (assuming the first option is "right" as per the options: right, acute, obtuse)