Question

A carpenter is building rectangular walls for a room addition. The width of a section wall is two times the height h. Each section has a brace that connects two opposite corners of the section. What is a simplified expression for the length of a brace?

Answer 1

Answer:

Length of Brace =  $x=\sqrt{5}h$

Step-by-step explanation:

The height is "h"

The width is 2 times that, so

Width is "2h"

The length of the brace is the diagonal from one corner to another. This length can be solved using pythagorean theorem, which will say:

Length^2 + Width^2 = length^2  [where length is length of brace, what we want]

Thus,

$(h)^2+(2h)^2=x^2$

Note:  Let "x" be the length of brace

Now, simplifying:

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

The expression for length of brace (x) is:  $x=\sqrt{5}h$