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

`√(2(a+b))=√(a+c)+√(a-c)`

Required:

We want to find the type of triangle

Step-by-step explanation:

First take square both side

`\begin{gathered} √(2(a+b))=√(a+c)+√(a-c) \\ 2a+2b=a+c+2√(a^2-c^2)+a-c \\ 2b=2√(a^2-c^2) \\ b=√(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