Question

fill in the blank 10 points
which of these triangles are right triang
6 in.
2.5 in.
6.5 in.
choose your answer_

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(c\) is the longest side (hypotenuse), and \(a, b\) are the other two sides.
Here, sides are \(2.5\) in, \(6\) in, \(6.5\) in. Longest side \(c = 6.5\), \(a = 2.5\), \(b = 6\).

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

\(a^2=(2.5)^2 = 6.25\), \(b^2 = 6^2=36\), so \(a^2 + b^2=6.25 + 36 = 42.25\).
\(c^2=(6.5)^2 = 42.25\).

Step3: Compare \(a^2 + b^2\) and \(c^2\)

Since \(2.5^2 + 6^2 = 6.5^2\) (both equal to \(42.25\)), by Pythagorean theorem, this triangle is a right triangle.

Answer:

This triangle (with sides 2.5 in, 6 in, 6.5 in) is a right triangle.