Answered

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Use the Pythagorean theorem to obtain the function​ D(x) for the length of the diagonal of a double square of width x.

Sagot :

MrRoyal

Answer:

[tex]D(x)= x\sqrt{2}[/tex]

Step-by-step explanation:

Given

[tex]Side = x[/tex]

Required

Represent the diagonal as a function

Using Pythagoras theorem, the diagonal is:

[tex]D^2= Side^2 + Side^2[/tex]

Substitute x for Side

[tex]D^2= x^2 + x^2[/tex]

[tex]D^2= 2x^2[/tex]

Take the square root of both sides

[tex]D= \sqrt{2x^2[/tex]

Split

[tex]D= \sqrt{2} * \sqrt{x^2[/tex]

[tex]D= \sqrt{2} * x[/tex]

[tex]D= x\sqrt{2}[/tex]

Express as a function.

[tex]D(x)= x\sqrt{2}[/tex]

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