Square Geometry Problem: Comparing Diagonal and Side Length Sums

Look at the square below:

333

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

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Step-by-step video solution

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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

Step-by-step written solution

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1

Understand the problem

Look at the square below:

333

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

3

Final Answer

No

Practice Quiz

Test your knowledge with interactive questions

Look at the triangle in the diagram. How long is side AB?

222333AAABBBCCC

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