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Write an equation relating the length of the legs of an isosceles​ triangle, x, to the length of the hypotenuse of the​ triangle, h. g

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Pythagorean TheoremIn a right triangle, the sum of the squares of the legs equals the square of the hypotenuse."Special Triangles"3-4-5
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8-15-17Converse of the Pythagorean ConjectureIf the lengths of a triangle satisfy the Pythagorean Theorem, then the triangle is a right triangle.Isosceles Right Triangle ConjectureIn an isosceles right triangle, if the legs have length x, then the hypotenuse has length x-root-2.30-60-90 Triangle ConjectureIn a 30-60-90 triangle, if the shorter leg has length x, then the longer leg has length x-root-3 and the hypotenuse has length 2x.Rationalizing the DenominatorEquation for a Circlea squared + b squared is less than c squaredObtuse trianglea squared + b squared is greater than c squaredAcute triangle
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An equation regarding the length of the sides of an isosceles right triangle is required.

The required equation is [tex]2x^2=h^2[/tex]

The length of the legs of triangle which are equal in length is [tex]x[/tex]

The length of the hypotenuse is [tex]h[/tex]

From the Pythagoras theorem we have

[tex]x^2+x^2=h^2\\\Rightarrow 2x^2=h^2[/tex]

Hence, in the above equation the length of the legs and the hypotenuse lengths are related.

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