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Answer:

25 in.

Step-by-step explanation:

DEC is a right triangle. <DEC is a right angle.

(DE)² + (EC)² = (DC)²

DE = ½DB = ½(48 in.) = 24 in.

(24 in.)² + (7 in.)² = (DC)²

576 in.² + 49 in.² = (DC)²

(DC)² = 625 in.²

DC = 25 in.