9514 1404 393
Answer:
24 cm^2
Step-by-step explanation:
The larger rectangle has dimensions in cm of 12 by (4+x). The smaller rectangle has dimensions of (x+2) by x. The area of the larger is 4 times the smaller, so ...
12(4+x) = 4(x)(x+2)
3(4+x) = x(x+2) . . . . . . divide by 4
x^2 +2x -3x -12 = 0 . . . eliminate parentheses, subtract 3(4+x)
(x -4)(x +3) = 0 . . . . . . . factor
The positive solution is x = 4, so the area of the smaller rectangle is ...
x(x+2) = 4(4+2) = 24 . . . cm^2
