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Properties of Isosceles and Equilateral Triangles

What is the p...

Question

What is the perimeter of a triangle if coordinates of its vertices are $(0, 0), (a, 0)$ and $(0, b)$

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Solution

$\begin{matrix} P o i n t B a t o r i g i n a n d p o i n t A a t y - a x i s a n d p o i n t B a t x - a x i s H e n c e, \Rightarrow A B = b, B C = a \Rightarrow A C = \sqrt{A B^{2} + B C^{2}} \Rightarrow A C = \sqrt{a^{2} + b^{2}} ∴ P e r i m e t e r o f Δ A B C = (a + b + \sqrt{a^{2} + b^{2}}) A n s . \end{matrix}$

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