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

The diagonal of the rectangle can be calculated by using the Pythagorean Theorem , because the diagonal and the two sides , length and width, of the rectangle , makes a right triangle .

Now we have the measure of length and width and we have to find the measure of diagonal

So according to the Pythagorean theorem

`d^2 = a^2 +b^2`

where , d is the diagonal , a is the length and b is the width

lets plug the values

`d^2 = 37^2 +60^2`

`d^2 = 1369+3600`

`d^2 = 4969`

Taking square root on both sides

d=70.49 Inches

d=70.5 inches

hence the length of one of the braces is 70.5 inches