If the square's area is 225 square centimeters, that means length of it's one side is 15 centimeters, because the formula for a square's area is [tex]{ a }^{ 2 }[/tex] where a is length side, in our case [tex]{ a }^{ 2 }=225[/tex] and [tex]\sqrt { { a }^{ 2 } } =\sqrt { 225 } \\ a=15[/tex]. So we know that one side's length is 15 we can find the diagonal. The solution is in the picture.
[tex]{ a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }\\ { 15 }^{ 2 }+{ 15 }^{ 2 }={ c }^{ 2 }\\ 225+225={ c }^{ 2 }\\ 550={ c }^{ 2 }\\ \sqrt { 550 } =\sqrt { { c }^{ 2 } } \\ \sqrt { 550 } =c\\ 15\sqrt { 2 } =c[/tex]
