Answer:
Length of tape required = 10 inches
Step-by-step explanation:
Length of the tape around the edge of the window = perimeter of the window
Since, distance between two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
For the side having extreme ends as (15, 18) and (21, 10),
[tex]d_1=\sqrt{(18-10)^2+(15-21)^2}[/tex]
[tex]=\sqrt{8^2+6^2}[/tex]
= 10 inches
Side with extreme ends (21, 10) and (15, 2),
[tex]d_2=\sqrt{(21-15)^2+(10-2)^2}[/tex]
[tex]=\sqrt{6^2+8^2}[/tex]
[tex]=\sqrt{100}[/tex]
= 10 inches
Distance between (15, 2) and (9, 10),
[tex]d_3=\sqrt{(15-9)^2+(2-10)^2}[/tex]
[tex]=\sqrt{(6)^2+(-8)^2}[/tex]
= 10 inches
Distance between (9, 10) and (15, 18),
[tex]d_4=\sqrt{(9-15)^2+(10-18)^2}[/tex]
[tex]=\sqrt{(-6)^2+(-8)^2}[/tex]
= 10 inches
Therefore, perimeter of the window = [tex]d_1+d_2+d_3+d_4[/tex]
= 10 + 10 + 10 + 10
= 40 inches
Length of tape required = 10 inches
