Answer:
see explanation
Step-by-step explanation:
Using Pythagoras' identity
The square on the hypotenuse of a right triangle is equal to the sum of the squares on the other 2 sides.
Consider the right triangle on the right and calculate n
n² + 2² = 3²
n² + 4 = 9 ( subtract 4 from both sides )
n² = 5 ( take the square root of both sides )
n = [tex]\sqrt{5}[/tex]
If the triangle on the left is right then the square of the longest side must equal the sum of the squares on the other 2 sides.
The longest side is n = [tex]\sqrt{5}[/tex] ⇒ n² = ([tex]\sqrt{5}[/tex] )² = 5 and
([tex]\sqrt{2}[/tex] )² + ([tex]\sqrt{3}[/tex] )² = 2 + 3 = 5
Hence D is a right angle
