Answer :
I think what they want is to use Pythagorean Theorem to determine if it's 90°.
The theorem states that, if a triangle has a right angle, the hypotenuse, called "c", relates to the other sides a and b as follows:
[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]
the diagonal of the square is the hypotenuse c, so therefore c = 13 in.
we'll make a = 5, and b = 12
[tex] {c}^{2} = {a}^{2} + {b}^{2} \\ \sqrt{ {c}^{2} } = \sqrt{( {a}^{2} + {b}^{2} ) } \\ c \: = \sqrt{( {a}^{2} + {b}^{2} ) } \\ 13= \sqrt{( {5}^{2} + {12}^{2} ) } [/tex]
[tex]13= \sqrt{( 25 + 144 ) } \\ 13= \sqrt{( 169 ) } = 13[/tex]
So it's true! since 13 = 13, the corner is in fact a right angle!!
The theorem states that, if a triangle has a right angle, the hypotenuse, called "c", relates to the other sides a and b as follows:
[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]
the diagonal of the square is the hypotenuse c, so therefore c = 13 in.
we'll make a = 5, and b = 12
[tex] {c}^{2} = {a}^{2} + {b}^{2} \\ \sqrt{ {c}^{2} } = \sqrt{( {a}^{2} + {b}^{2} ) } \\ c \: = \sqrt{( {a}^{2} + {b}^{2} ) } \\ 13= \sqrt{( {5}^{2} + {12}^{2} ) } [/tex]
[tex]13= \sqrt{( 25 + 144 ) } \\ 13= \sqrt{( 169 ) } = 13[/tex]
So it's true! since 13 = 13, the corner is in fact a right angle!!