Problem

Use the displayed diagrams to interpret \(A=x(12-x)\) for a rectangle with positive side lengths. Explain both factors and area units, find the boundary zeros, and distinguish degenerate zero-area cases from the valid domain \(0<x<12\).

Source rectangle model for A=x(12−x) square units with positive side lengths and domain 0<x<12; no zero-validity conclusion is shown.

Answer choices

Choose your path.

Preview only

Factor x is one side length and 12 − x is the other; their product is area. For 0 < x < 12, zeros 0 and 12 are degenerate boundary cases with area zero, not valid positive-area rectangles.

Factor x is one side and 12 − x is the other; their product is area. The zero x = 12 is selected as a valid positive-area rectangle because it is an algebraic solution.

Factor x and 12 − x are side lengths; their operation adds lengths, so A is a length. Zeros 0 and 12 are interpreted as maximum areas.

Factor x is one side and 12 − x is the other; their product is area. The zero x = 0 is rejected as algebraically invalid rather than recognized as a degenerate boundary case.

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

Use the displayed diagrams to interpret \(A=x(12-x)\) for a rectangle with positive side lengths. Explain both factors and area units, find the boundary zeros, and distinguish degenerate zero-area cases from the valid domain \(0<x<12\).

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.