Question

Help please help me its a hard one

Answer 1

The sum of a and b is 12.

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 )

=
`√((2-0)^2+(5-1)^2)`

=
`√((2)^2+(4)^2)`

=
`√(4+16)`

=
`√(20)` =
`2√(5)`

Distance between points ( 2, 5 ) and ( 7, 0 )

=
`√((7-2)^2+(0-5)^2)`

=
`√(5^2+(-5)^2)`

=
`√(25+25)`

=
`√(50)` =
`5√(2)`

And you can calculate the distance between points ( 0, 1 ) and ( 7, 0 ) to be exactly
`5√(2)` as well. Therefore, you can say that the perimeter of this triangle is
`2(5√(2)) + 2√(5)` =
`10√(2) + 2√(5)`. Note that this is similar to the form we are given. Thus, a = 10, and b = 2 - making it's sum 10 + 2 = 12.