Given that quadrilaterals ABCD, LMNO, and STUV are all equal, and that STUV is a rectangle with diagonal SU measuring 5 cm, we can determine the lengths of the diagonals AC and BD.
In a rectangle, the diagonals are equal in length and can be calculated using the Pythagorean theorem. Since a rectangle has two equal diagonals, we have:
\[ d = \sqrt{length^2 + width^2} \]
However, we know the length of the diagonal SU is 5 cm. Therefore, the lengths of the diagonals in rectangle STUV are equal to 5 cm:
\[ SU = TV = 5 \text{ cm} \]
Since quadrilateral ABCD is equal to quadrilateral STUV, it follows that the diagonals AC and BD of quadrilateral ABCD are also equal in length to the diagonals of quadrilateral STUV.
Thus, we have:
\[ AC = BD = 5 \text{ cm} \]
Therefore, the lengths of diagonals AC and BD are both 5 cm.
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