Square Geometry: Comparing Diagonal Sum vs Side Lengths in a 6-Unit Square

Question

Look at the square below:

Is the sum of the two diagonals greater than the sum of the 3 sides of the square?

00:00 Is the sum of diagonals greater than the sum of 3 sides of the square?

00:03 In a square all sides are equal

00:08 Let's use the Pythagorean theorem in triangle BCD

00:12 Let's substitute appropriate values and solve for BD

00:21 This is the length of diagonal BD

00:25 In a square the diagonals are equal

00:28 Let's calculate the sum of diagonals

00:31 Let's substitute appropriate values and solve for the sum

00:39 Let's calculate the sum of 3 sides of the square

00:46 Let's substitute appropriate values in the equation

00:53 And this is the solution to the question