Question

Find the perimeter of the triangle with vertices (0,8),(6,0) and origin (9,3),(1,-3) and origin

Answer 1

Formula used: Distance between two point (a, b) and (c, d) = $\sqrt{(a-b)^{2} + (c-d)^{2}}$

Using the formula

(1) A(0, 0), B(0, 8), C(6, 0)
AB = 8
AC = 6
BC = 10

So perimeter = (8 + 6 + 10) / 3 = 24 / 3 = 8

(2) A(0, 0), B(1, -3), C(9, 3)
AB = $\sqrt{10}$
AC = 3$\sqrt{10}$
BC = 10

So perimeter = ($\sqrt{10}$ + 3$\sqrt{10}$ + 10) / 3 = $\frac{10 + 4\sqrt{10}}{3} \\ \\ \frac{9 + 3\sqrt{10}}{3} + \frac{1 + \sqrt{10}}{3} \\ \\ 3 + \sqrt{10} + \frac{1 + \sqrt{10}}{3}$