Question

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

The value of x in terms of l is

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

Data given;

Length = l

width = 2l

diagonal = x

assuming we cut a section across the diagonal, we would have a right angle triangle. we can solve the right angle triangle using Pythagoras Theorem.

Pythagoras Theorem

This formula is used to find the missing side of a right angle triangle where x is equal to it's longest side i.e the hypothenuse.

The square of the hypothenuse is equal to the sum of the square of it's two sides.

substituting the values

$x^2 = l^2 + (2l)^2\\x^2 = l2 + 4l^2\\x^2 = 5l^2\\\\x = \sqrt{5l^2}$

From the calculation above, we have x in terms of l as

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

Learn more on rectangles and Pythagoras theorem here;

brainly.com/question/654982