Determine if Triangle with Sides 2, 4, and 5 is Right-Angled

To determine if the triangle is right-angled, we apply the Pythagorean Theorem as follows:

• Identify the sides: $a = 2$, $b = 4$, and $c = 5$ (longest side).
• Apply the Pythagorean Theorem: check if $2^2 + 4^2 = 5^2$.

Calculate:
$2^2 = 4$
$4^2 = 16$
Sum: $4 + 16 = 20$

Next, calculate $5^2 = 25$.

Compare: $20 \neq 25$.

Since $20 \neq 25$, the inequality confirms the triangle is not right-angled.

The triangle is not right-angled, thus the correct answer is No.