A carpenter builds a rectangular bookcase that is 40 inches long and 55 inches tall. The carpenter uses two braces along the diagonals to support the bookcase.

The length of each brace, to the nearest inch, is ___ inches.

lel12 Mar 30, 2021

#1**+3 **

The braces are the hypotenuse of a right triangle with legs of 40 and 55 in

brace^{2} = 40^{2 }+ 55^{2}

brace =~~ 68 in

ElectricPavlov Mar 30, 2021

#1**+3 **

Best Answer

The braces are the hypotenuse of a right triangle with legs of 40 and 55 in

brace^{2} = 40^{2 }+ 55^{2}

brace =~~ 68 in

ElectricPavlov Mar 30, 2021

#2**+2 **

*A carpenter builds a rectangular bookcase that is 40 inches long and 55 inches tall. The carpenter uses two braces along the diagonals to support the bookcase.*

If you draw this, or just picture it in your mind, you recognize that the diagonal brace forms the hypotenuse of a right triangle whose legs are 40 inches and 55 inches. So, it's possible just to use Pythagoras' Theorem.

Call the 40 inch side as "a" Call the 55 inch side as "b" Call the brace (hypotenuse) as "c"

By the theorem, a^{2} + b^{2} = c^{2}

So c^{2} = 40^{2} + 55^{2}

c^{2} = 1600 + 3025 = 4625

c = sqrt(4625)

c = __+__68**.**007

Thus, the length of each brace is **68 inches**

_{.}

Guest Mar 30, 2021