Find the perimeter of a triangle whose vertices pass through ( 3, 2), (4, 5) and (6, 2) in surd form.
A
3 + \(\sqrt{12} + \sqrt{13}\)
B
3 - \(\sqrt{10} + \sqrt{13}\)
C
3 + \(\sqrt{10} + \sqrt{13}\)
D
3 - \(\sqrt{12} + \sqrt{13}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
From the diagram above, Calculate the distance between any two vertices as follows.
PQ = \(\sqrt{(6 - 3)^2 + (2-2)^2}\) = \(\sqrt{9}\) = 3
QR = \(\sqrt{(6 - 4)^2 + (2-5)^2}\) = \(\sqrt{13}\)
PR = \(\sqrt{(4 - 3)^2 + (5 - 1)^2}\) = \(\sqrt{10}\)
\(\therefore\), perimeter = 3 + \(\sqrt{13}\) + \(\sqrt{10}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #70253)