Question

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

Answer 1

Answer:

$D(x)= x\sqrt{2}$

Step-by-step explanation:

Given

$Side = x$

Required

Represent the diagonal as a function

Using Pythagoras theorem, the diagonal is:

$D^2= Side^2 + Side^2$

Substitute x for Side

$D^2= x^2 + x^2$

$D^2= 2x^2$

Take the square root of both sides

$D= \sqrt{2x^2$

Split

$D= \sqrt{2} * \sqrt{x^2$

$D= \sqrt{2} * x$

$D= x\sqrt{2}$

Express as a function.

$D(x)= x\sqrt{2}$