Question

In a triangle the sum of two sides is $x$ and their product is $y$ such that $(x+z)(x-z)=y$ where $z$ is the third side of the triangle.

Square of the length of the third side of the triangle is

• A. $x^2+y$
• B. $x^2-y$
• C. $x^2+y^2$
• D. $x-y^2$

Answer 1

The correct option is B $x^2-y$

Given that, $z$ is the third side of the triangle.

Also given, $(x+z)(x-z)=y$

$\Rightarrow x(x-z)+z(x-z)=y$

$\Rightarrow x^2-xz+xz-z^2=y$
$\Rightarrow x^2-z^2=y$
Therefore, $z^2=x^2-y$