Question

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A restaurant uses rectangular napkins where the length, l, is twice as long as the width. The length of the napkin along the diagonal is x. What is x in terms of l? Replace a and b with the correct values.

Answer 1

Using the Pythagorean Theorem, it is found that x in terms of l is given by:

$x = l\frac{\sqrt{5}}{2}$

What is the Pythagorean Theorem?

• The Pythagorean Theorem relates the length of the legs $l_1$ and  $l_2$ of a right triangle with the length of the hypotenuse h, according to the following equation:

$h^2 = l_1^2 + l_2^2$

In a rectangle:

• The diagonal x is the hypotenuse, hence $h = x$.

• The legs are the sides.

• Length l, twice as long as the width, hence $l_1 = l, l_2 = \frac{l}{2}$, and:

$h^2 = l_1^2 + l_2^2$

$x^2 = l^2 + \frac{l^2}{4}$

$x^2 = \frac{5l^2}{4}$

$x = \sqrt{\frac{5l^2}{4}}$

$x = l\frac{\sqrt{5}}{2}$

To learn more about the Pythagorean Theorem, you can take a look at https://brainly.com/question/654982