if ABCD is a square and DB is equal to 12 cm, then AC is equal to 6 cm.
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"if ABCD is a square and DB is equal to 12 cm, then AC is equal to 6 cm."
No it isn't.
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To determine the length of AC (the diagonal of square ABCD), we can use the Pythagorean theorem. Since ABCD is a square, all sides and angles are equal.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, we can consider triangle ADB, where AD and AB are the two sides, and DB is the hypotenuse (diagonal).
Let's denote the length of AC as x. Since AC is the diagonal of the square, it will be equal to the hypotenuse of any of the right triangles formed within the square.
Using the Pythagorean theorem, we have:
(AD)^2 + (DB)^2 = (AB)^2
Since ABCD is a square, AD is equal to AB.
AB^2 + (12 cm)^2 = x^2
Therefore, AC^2 = AB^2 + (12 cm)^2
Since AD = AB, we can write:
AC^2 = (AD)^2 + (12 cm)^2
To solve for AC, we need to calculate the square root of both sides:
AC = sqrt((AD)^2 + (12 cm)^2)
Since AD is equal to AB, we have:
AC = sqrt((AB)^2 + (12 cm)^2)
Given that DB (or AB) is equal to 12 cm, we can substitute this value:
AC = sqrt((12 cm)^2 + (12 cm)^2)
Calculating this expression gives:
AC = sqrt(144 cm^2 + 144 cm^2)
AC = sqrt(288 cm^2)
AC ≈ 16.97 cm
Therefore, AC is approximately 16.97 cm, not 6 cm.