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.)

So I first applied the 45 45 90 special right triangle and then I came up with x/1= square root of 3.23/ square root of 2. Since this represents the base and the height of the triangle I plugged the values into the area of a triangle formula and solved. Is this accurate?
greenlight-admin's picture

Your solution is perfectly reasoned! Great work!

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