Question

What is the length of the one of the braces, to the nearest tenth of a centimeter?

A carpenter builds a rectangular bookcase that is 120 cm long and 62 cm 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 centimeter?

Enter your answer as a decimal in the box.

cm

Answer 1

`135.1cm`

Explanation:

pythagoras' theorem: `a^2 + b^2 = c^2`

`c` is the length of a diagonal, while `a` and `b` are the lengths of the sides of the rectangle.

`120^2 + 62^2 = c^2`

`c^2 = 14400 + 3844 = 18244`

`c = sqrt(18244) = 135.070...`

the length of the diagonal is `135.1cm` (to the nearest `0.1cm`)

the length of one of the braces is `135.1cm`