Question

How do you find the length of the diagonal of a rectangle whose length is 6 meters and whose width is 4 meters in simple radical form?

Answer 1

The length of the diagonal is `2sqrt13` meters or about `7.21` meters in decimal form (rounded to nearest hundredth's place).

Explanation:

The diagonal of a rectangle plus two adjacent sides make a triangle. That "diagonal" is the same as the hypotenuse in a right triangle. Since we have the length and width and want the hypotenuse, we can use the Pythagorean Theorem shown below to solve it:

Following this image, we know that
`color(red)(6)^2 + color(limegreen)(4)^2 = color(blue)c^2`

Simplify the left hand side:
`36 + 16 = c^2`

`52 = c^2`

Take the square root of both sides:
`sqrt(52) = sqrt(c^2)`

`c = sqrt52`

#c = sqrt(4 * 13)

`c = sqrt4sqrt13`

`c = 2sqrt13`

The length of the diagonal is `2sqrt13` meters or about `7.21` meters in decimal form (rounded to nearest hundredth's place).

Hope this helps!