Question

question: 10
a rectangular garden will be surrounded with two different types of the plants to a certain distance. the length of the plants will be as shown by the graphs.
which graph represents the solution set for the perimeter addition to area comparison, by 40% of the path is fixed?
(there are two graphs with radio buttons labeled a and b, showing geometric figures on grids)

Explanation:

Step1: Analyze the problem context

The problem involves a graph related to a parachute's descent (length vs. time, with slope representing speed). We need to identify which graph shows a slower speed (since slope = speed, a smaller slope means slower speed).

Step2: Compare the slopes of the two graphs

• For a line (or the edge of the shaded region representing the parachute's path), the slope is calculated as $\frac{\text{rise}}{\text{run}}$.
• In the first graph (A), the slope of the relevant edge (e.g., the boundary of the shaded area) appears steeper. In the second graph (B), the slope of the corresponding edge is less steep.
• A less steep slope means a smaller rate of change of length with respect to time, i.e., slower speed.

Answer:

The graph labeled B (the lower graph) represents the solution where the parachute is slower, as its slope (representing speed) is smaller.