Question

Suppose you are given a triangle with hypotenuse of length 2.5 and legs of length x−1 and x+1.

Answer 1

The value for the given right triangle of $x$ is $\pm \sqrt{2}$.

How to find the value of a variable

By Pythagorean theorem and some algebraic handling, we have the following second order polynomial:

$(x-1)^{2}+(x+1)^{2} = 2.5^{2}$ (1)

Where $x$ is the desired variable.

$(x^{2}-2\cdot x +1)+(x^{2}+2\cdot x +1) = 2.5^{2}$

$2\cdot x^{2}+2 = 2.5^{2}$

$2\cdot x^{2}-4.25= 0$

$x = \pm \sqrt{2}$

The value for the given right triangle of $x$ is $\pm \sqrt{2}$. $\blacksquare$

Remark

The statement is incomplete. Correct form is shown below:

Suppose you are given a triangle with hypotenuse of length 2.5 and legs of length $x-1$ and $x+1$. Determine the value of $x$.

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