Let
[tex]a=2\ in\\b=4\ in\\c=5\ in[/tex]
we know that
If [tex]c^{2} =a^{2}+b^{2}[/tex] -----> is a right triangle
If [tex]c^{2} > a^{2}+b^{2}[/tex] -----> is an obtuse triangle
If [tex]c^{2} < a^{2}+b^{2}[/tex] -----> is an acute triangle
so
substitute the values
[tex]5^{2} > 2^{2}+4^{2}[/tex] ------> is an obtuse triangle
therefore
the answer is
The triangle is not acute because [tex] 2^{2}+4^{2}< 5^{2}[/tex]
Answer: The correct option is
(C) The triangle is not acute because 2² + 4² < 5².
Step-by-step explanation: We are to select the statement that best explains the type of the triangle having lengths of three sides as 2 inch, 5 inch and 4 inch.
We know that a triangle with side lengths a, b and c (c > a, b)is
(i) an acute-angled if a² + b² > c², and
(ii) an obtuse-angled if a² + b² < c².
For the given triangle,
a = 2 inch, b = 4 inch and c = 5 inch.
So, we have
[tex]a^2+b^2=2^2+4^2=4+16=20,\\\\c^2=5^2=25.[/tex]
Since,
[tex]20<25\\\\\Rightarrow a^2+b^2<c^2,[/tex]
so the given triangle is not acute, but obtuse.
Thus, the triangle is not acute because 2² + 4² < 5².
Option (C) is correct.
