Answer:
= 4√53 units
that is option(a)
Step-by-step explanation:
all sides of the square are of the same length
so if we get the length if this side, we can calculate its perimeter
there's this formula,
side length between two points, let's say A(x, y) and B(p, q), is equal to
[tex] \mathsf{ \sqrt{ {(x - p)}^{2} + {(y - q)}^{2} } }[/tex]
so here we go,
the same points A and B here are
(4, 7) and (-3, 5)
therefore, side length :-
[tex] = \mathsf{ \sqrt{( {7 - 5})^{2} + {(4 - ( - 3))}^{2} } } [/tex]
[tex] = \mathsf{ \sqrt{ {2}^{2} + {7}^{2} } } [/tex]
[tex] = \mathsf{ \sqrt{4 + 49} } [/tex]
[tex] = \mathsf{\sqrt{53} }[/tex]
the side length comes out to be √(53)
now perimeter of a square is
4 × side length
= 4√53 units
