Question 156516
I think instead of:
L(0,1)M(3,5)N(5,5)P(5,1)
.
you meant:
L(3,1)M(3,5)N(5,5)P(5,1)
.
It would be best to plot all four points onto graph paper.  Once you do that, it will be easy to see that:
width of the rectangle is between either:
LP or MN
.
whereas the length of the rectangle is between either:
LM or PN
.
Calculating the width.  Let's use:M and N
M(3,5)N(5,5)
You can either see the distance visually from the graph or use the distance formula:
distance = sqrt[(x2-x1)^2 + (y2-y1)^2]
distance = sqrt[(5-3)^2 + (5-5)^2]
distance = sqrt[(2)^2 + (0)^2]
distance = sqrt[4 + 0]
distance = sqrt[4]
distance = 2 (width)
.
Calculating the length.  Let's use:P and N
P(5,1)N(5,5)
You can either see the distance visually from the graph or use the distance formula:
distance = sqrt[(x2-x1)^2 + (y2-y1)^2]
distance = sqrt[(5-5)^2 + (5-1)^2]
distance = sqrt[(0)^2 + (4)^2]
distance = sqrt[0 + 16]
distance = sqrt[16]
distance = 4 (length)
.
Perimeter = 2(w+l) = 2(2+4) = 2(6) = 12 units
area = wl = 2(4) = 8 square units