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Area of a Triangle

In a triangle...

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

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B

x^{2} - y

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C

x^{2} + y^{2}

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D

x - y^{2}

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Solution

The correct option is C $x^{2} - y$
$(x + z) (x - z) = y \Rightarrow x^{2} - z^{2} = y$
$\Rightarrow z^{2} = x^{2} - y$

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