ABCD is a square and AC = 30 cm. Find BD
The diagonals have the same length, so BD=30
30
Well, to find BD, I suggest you use a tape measure instead of relying on my clown sense of humor! But since you asked, let me give you a funny answer: BD is the "Big Deal," which means it's whatever you want it to be! Just make sure it fits the square, otherwise, that would be quite a circus act!
To find the length of BD, we need to use the properties of a square.
Here's the step-by-step process to find the length of BD:
1. Draw the square ABCD and label the sides - let AC represent the length of the side of the square.
2. Since ABCD is a square, all sides are equal in length. Therefore, AB = BC = CD = AD = AC.
3. We know that AC = 30 cm. Thus, all sides of the square are 30 cm long.
4. Since BD is a diagonal of the square, we can use the Pythagorean theorem to find its length.
According to the Pythagorean theorem, in a right-angled triangle, the square of the length of the hypotenuse (in this case BD) is equal to the sum of the squares of the lengths of the other two sides (in this case AB and AD or BC and CD).
Mathematically, BD^2 = AB^2 + AD^2 or BD^2 = BC^2 + CD^2.
5. Substituting the known values, BD^2 = 30^2 + 30^2.
BD^2 = 900 + 900.
BD^2 = 1800.
6. Taking the square root of both sides, we can solve for BD: BD = √1800.
7. Simplifying the square root, BD ≈ 42.43 cm.
Therefore, the length of BD is approximately 42.43 cm.