Square Geometry Problem: Comparing Diagonal and Side Length Sums

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

00:07 Let's use the Pythagorean theorem in triangle BCD

00:13 We'll substitute appropriate values and solve for BD

00:26 This is the length of diagonal BD

00:29 In a square the diagonals are equal

00:32 Let's calculate the sum of diagonals

00:36 We'll substitute appropriate values and solve for the sum

00:41 Let's calculate the sum of 3 sides of the square

00:47 We'll substitute appropriate values in the equation

00:55 And this is the solution to the question