Question

If a triangle has sides measuring 60, 75, 45, is it a right angle?

A. Yes because 5,625 equals 5,625
B. Yes because 3,600 equals 3,600
C. No because 9,225 doesn’t equal 2,025
D. No because 5,625 doesnt equal 3,600

Answer 1

To determine if a triangle with sides measuring 60, 75, and 45 is a right triangle, we can use the Pythagorean theorem. According to the theorem, for a triangle with sides \(a\), \(b\), and \(c\) (where \(c\) is the longest side), the triangle is a right triangle if:

\[
a^2 + b^2 = c^2
\]

First, we identify the longest side, which is 75. Thus, \(a = 60\), \(b = 45\), and \(c = 75\).

Next, we calculate \(a^2\), \(b^2\), and \(c^2\):

\[
60^2 = 3600
\]
\[
45^2 = 2025
\]
\[
75^2 = 5625
\]

Now we can check if the Pythagorean theorem holds:

\[
3600 + 2025 = 5625
\]

Since \(5625 = 5625\), the condition holds true, and the triangle is a right triangle.

Thus, the correct answer is **A. Yes because 5,625 equals 5,625**.