Answer:
The sum of a and b is 12.
Step-by-step explanation:
Try drawing this figure. ABCD would actually be a triangle, rather than the common quadrilateral you would expect - considering there are 4 points plotted. Therefore, we would have to find the distance between respective points ( 0, 1 ) and ( 2, 5 ) / ( 2, 5 ) and ( 7, 0 ) / ( 0, 1 ) and ( 7, 0 ). Let's apply the distance formula and calculate the distance between each point, therefore determining the perimeter.
Distance between points ( 0, 1 ) and ( 2, 5 )
= [tex]\sqrt{(2-0)^2+(5-1)^2}[/tex]
= [tex]\sqrt{(2)^2+(4)^2}[/tex]
= [tex]\sqrt{4+16}[/tex]
= [tex]\sqrt{20}[/tex] = [tex]2\sqrt{5}[/tex]
Distance between points ( 2, 5 ) and ( 7, 0 )
= [tex]\sqrt{(7-2)^2+(0-5)^2}[/tex]
= [tex]\sqrt{5^2+(-5)^2}[/tex]
= [tex]\sqrt{25+25}[/tex]
= [tex]\sqrt{50}[/tex] = [tex]5\sqrt{2}[/tex]
And you can calculate the distance between points ( 0, 1 ) and ( 7, 0 ) to be exactly [tex]5\sqrt{2}[/tex] as well. Therefore, you can say that the perimeter of this triangle is [tex]2(5\sqrt{2}) + 2\sqrt{5}[/tex] = [tex]10\sqrt{2} + 2\sqrt{5}[/tex]. Note that this is similar to the form we are given. Thus, a = 10, and b = 2 - making it's sum 10 + 2 = 12.
