Respuesta :
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
[tex]=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The distance between P and Q is
[tex]=\sqrt{(6-2)^2+(2-2)^2}[/tex] in
[tex]=\sqrt {4^2+0^2}[/tex] in
=4 in
The distance between Q and R is
[tex]=\sqrt{(6-6)^2+(5-2)^2[/tex] in
[tex]=\sqrt{0^2+3^2}[/tex] in
=3 in
The distance between R and S is
[tex]=\sqrt{(2-6)^2+(5-5)^2}[/tex] in
[tex]=\sqrt{ (-4)^2}[/tex] in
=4 in
The distance between S and P is
[tex]=\sqrt{(2-2)^2+(2-5)^2}[/tex] in
[tex]=\sqrt{(-3)^2}[/tex] 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
