Question: Diagonal of a Square

Comment on Diagonal of a Square

I set up √3.23 as equal to 2x as the hypotenuse in a 45-45-90 triangle, meaning each leg of the triangle (and therefore each side of the square) would equal root 3.23 over 2. To figure out the area of the square, I multiplied this quantity by itself, and got 3.23/4. Where did I go wrong?
greenlight-admin's picture

Be careful. The sides of a 45-45-90 triangle will be in the form x, x, (√2)x (not 2x as you have suggested)

So, we can write √3.23 = (√2)x

Hello Brent. I applied the concept of similar triangles (1-1-and √2. I obtained the same answer. Thanks.
greenlight-admin's picture


Hi Brent,
Can we take the formula diagonal 1 *diagonal 2 /2 formula. Since all four sides are equal, so the 2 diagonals will be equal? Is this correct?
greenlight-admin's picture

Great idea.

You're referring to the property described at 5:10 of this videos:

So, for column A, the area = (√3.23)(√3.23)/2 = 3.23/2
Column B: 3.23

So, column B is greater.

So the two diagonals will be equal for square and rhombus?
greenlight-admin's picture

The two diagonals will be equal for all squares. However, the diagonals are equal in a rhombus ONLY IF the angles in the rhombus are all 90 degrees (that is, the rhombus is a square.)

Have a question about this video?

Post your question in the Comment section below, and a GRE expert will answer it as fast as humanly possible.

Change Playback Speed

You have the option of watching the videos at various speeds (25% faster, 50% faster, etc). To change the playback speed, click the settings icon on the right side of the video status bar.

Let me Know

Have a suggestion to make the course even better? Email us today!

Free “Question of the Day” emails!