What is the perimeter of a polygon abcd vertex a(5,12) b(9,9) c(12,5) d(0,0)
1 answer:
Answer:
36
Step-by-step explanation:
We have to compute 4 distances and then add them up.
It may help to draw this first to see which distances to compute.
So I'm going to start with computing the distance from (0,0) to (5,12), then from (5,12) to (9,9), then from (9,9) to (12,5), and then finally from (12,5) to (0,0).
So distance from (0,0) to (5,12)
d=sqrt((5-0)^2+(12-0)^2)=sqrt(25+144)=sqrt(169)=13
Distance from (5,12) to (9,9)
d=sqrt((9-5)^2+(12-9)^2)=sqrt(4^2+3^2)=sqrt(16+9)=sqrt(25)=5
Distance from (9,9) to (12,5)
d=sqrt((12-9)^2+(9-5)^2)=sqrt(3^2+4^2)=sqrt(9+16)=sqrt(25)=5
Distance from (12,5) to (0,0)
d=sqrt((12-0)^2+(5-0)^2)=sqrt(12^2+5^2)=sqrt(144+25)=sqrt(169)=13.
Up all of our distances 13+5+5+13=(13+13)+(5+5)=26+10=36
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Remainder Theorem says that if there is any Polynomial equation P(x), which is to be divided by (x - a) then remainder can be calculated by substituting value of a in equation P(x).
= P(x) divided by
Step 1: Find a
To find a we will have to convert (x+2) into (x - a) form
i.e. (x+2) = (x - (-2))
therefore, a = -2
Step 2: Substitute value of a in P(x),
By substitution we get,
=
=
= = Remainder
Hence, Remainder is 55.