Question

If a, b and c represent the side lengths of a triangle and √2(a + b) = √a+c+ √a-c what type of triangle is it?

Answer 1

Given:

The given expression is

$\sqrt{2(a+b)}=\sqrt{a+c}+\sqrt{a-c}$

Required:

We want to find the type of triangle

Explanation:

First take square both side

$\begin{gathered} \sqrt{2(a+b)}=\sqrt{a+c}+\sqrt{a-c} \\ 2a+2b=a+c+2\sqrt{a^2-c^2}+a-c \\ 2b=2\sqrt{a^2-c^2} \\ b=\sqrt{a^2-c^2} \end{gathered}$

now again take square for both side

$\begin{gathered} b^2=a^2-c^2 \\ a^2=b^2+c^2 \end{gathered}$

Final answer:

Right angle triangle