Answer:
400 cm²
Step-by-step explanation:
Let s represent the length of the side of the square in cm. Then the rectangle dimensions are (s-2) and (s+5), and the relation given by the problem statement is ...
s² = (s -2)(s +5) -50
s² = s² +3s -60 . . . . . . eliminate parentheses
3s = 60 . . . . . . . . . . . . add 60-s²
60/3 = s = 20 . . . . . . . the side length of the square is 20 cm.
The area of the square is (20 cm)² = 400 cm².
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Check
The dimensions of the rectangle are 18 cm by 25 cm, so its area is 450 cm². The area of the square is 50 cm² smaller than that, as required.
