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?

1 Answer
May 29, 2018

Answer:

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:
study.com

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!