Verified Answer :

Aliwohaish12

a^2+b^2=c^2 is a right angled triangle.

You're given that a^2+b^2>c^2
cos(A) = [a^2+b^2-c^2]/2ab
c^2+2abcos(A) = a^2+b^2
Thus, c^2+2abcos(A) > c^2
cos(A)>0
A>90 degrees. ie Obtuse triangle.

If a^2+b^2 < c^2.
A<90 degrees ie. Acute triangle.
Hypotenuse is c.

Use the law of cosines.

apologiabiology

angles corespond with legnth of side
angle oposite a is obtuse
osbtuse meas move than 90
all angles in a triangle add to 180
180/2=90
since that angle oposite a is bigger than half, that angle is bigger than the oterh angles
so therefor
a>b
a>c


we know that from pythagoran theorem that the square of the longest side is equal to the squares of the other 2 sides
the angle oposite that longest side is 90
obtuse>90 so it is longer legnth
a is longest side
b^2+c^2<a^2

the answer is D