Question

A carpenter builds a rectangular bookcase that is 37 inches long and 60 inches tall. the carpenter uses two braces along the diagonals to support the bookcase. what is the length of the one of the braces, to the nearest tenth of a inch?

Answer 1

Since the shape of the bookcase is rectangular, the length of both diagonals will be the same. Making a diagonal in the rectangle divides it into two equal Right Angled Triangles. Using the pythagorean theorem we can find the length of the diagonal. The image of the scenario is shown below.The diagonal forms the hypotenuse of the right triangle with two legs of 37 inches and 60 inches. So applying the Pythagorean Theorem, we get:

$diagonal=\sqrt{ 37^{2} + 60^{2} }= \sqrt{4969} = 70.5$

So the length of the brace along the diagonal will be 70.5 rounded to tenth of an inch.