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A rectangle has a length that is twice its width. If the perimeter is 36 cm, find the dimensions of the rectangle.
The formula for perimeter is \(P = 2(\text{length} + \text{width})\).
Substituting the expression for length, \(36 = 2(2w + w) = 6w\).
Divide by 6: \(w = 36 / 6 = 6\).
The length is \(2w = 2 \times 6 = 12\).
#### Width: 6 cm, Length: 12 cm
If \(f(x) = x^2 - 4x + 4\), find \(f(3)\).
Substitute \(x = 3\) into the function: \(f(3) = 3^2 - 4 \times 3 + 4\).
Simplify: \(f(3) = 9 - 12 + 4 = 1\).
#### \(f(3) = 1\)