Question

What is the length of the diagonal of a rectangle with a length of 6 in. and a width of 4 in.?

Answer 1

The diagonal is `sqrt(52).`

Explanation:

We can start by establishing that a rectangle has 4 right angles. This is essential in finding the diagonal length. To find the diagonal length we can use the Pythagorean theorem.

To do this we can simply draw an imaginary line from one corner to the opposite corner. We can still use the side lengths since we didn't change anything about them.

As you can see we've created a right triangle, either in the top right or the bottom left. From here we can use the Pythagorean theorem with the two leg, to find the hypotenuse, which will be the diagonal measure.

We have `6^2 + 4^2 = c^2`. That is `36 + 16 = c^2`. When we solve we get `c^2 = 52`. To get it by itself, we square root each side.

`sqrt(c^2)=sqrt(52) => c = sqrt(52)`.