Rouge Rope
A rectangle A of 7 cm. width and 21 length is surrounded by a rope of the perimeter's length. Then the same rope is relocated to border rectangle B and square C such that rectangles A & B are similar as shown.
What is the smallest total areas of rectangle B and square C in ?
The answer is 84.
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1 solution
The rope's length = rectangle's perimeter = 2(7+21) = 56.
If we let x = rectangle B's width, B's length = 3x. Hence, square C's side = (56 - 8x)/4 = 14 - 2x.
f(x) = total areas of B+C = 3 x 2 + ( 1 4 − 2 x ) 2 = 7 x 2 - 56x + 196
f '(x) = 14x - 56 = 0; x = 4. So the minimum is at f(4) = 84.