Question

One side of a square has endpoints (4.7) and (-3,5). What is the perimeter of the square?

Answer 1

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

$\mathsf{ \sqrt{ {(x - p)}^{2} + {(y - q)}^{2} } }$

so here we go,

the same points A and B here are

(4, 7) and (-3, 5)

therefore, side length :-

$= \mathsf{ \sqrt{( {7 - 5})^{2} + {(4 - ( - 3))}^{2} } }$

$= \mathsf{ \sqrt{ {2}^{2} + {7}^{2} } }$

$= \mathsf{ \sqrt{4 + 49} }$

$= \mathsf{\sqrt{53} }$

the side length comes out to be √(53)

now perimeter of a square is

4 × side length

= 4√53 units