Question

The coordinates of the points bellow represent the vertices of a rectangle: P: (2,2). Q:(6,2) R:(6,5) S:(2,5) What is the perimeter, in units, of rectangle PQRS

Answer 1

Answer:

Therefore the value of perimeter of the rectangle is 14 in.

Step-by-step explanation:

The opposite sides of a rectangle are congruent.

The perimeter of a rectangle is 2(length + width)

The area of a rectangle is (length×width).

Given the vertices of a rectangle are P(2,2), Q(6,2), R(6,5) and S(2,5).

To find the the perimeter, first we need the sides of the rectangle.

The distance between two points(x₁,y₁) and (x₂,y₂) is

$=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The distance between P and Q is

$=\sqrt{(6-2)^2+(2-2)^2}$  in

$=\sqrt {4^2+0^2}$ in

=4 in

The distance between Q and R is

$=\sqrt{(6-6)^2+(5-2)^2$ in

$=\sqrt{0^2+3^2}$ in

=3 in

The distance between R and S is

$=\sqrt{(2-6)^2+(5-5)^2}$ in

$=\sqrt{ (-4)^2}$ in

=4 in

The distance between S and P is

$=\sqrt{(2-2)^2+(2-5)^2}$ in

$=\sqrt{(-3)^2}$ in

=3 in

Therefore the length of the rectangle is = 4 in.

an the width of the rectangle is = 3 in

Therefore the perimeter of the rectangle is =2(4+3) in

                                                                        =14 in