Question

the figure below is the graph of the dimensions of a rectangle whose adjacent side lengths exhibit inverse variation. a. true b. false

Explanation:

Step1: Recall the formula for inverse variation

For two variables \(x\) and \(y\) that are inversely - proportional, the formula is \(y=\frac{k}{x}\) or \(k = xy\), where \(k\) is the constant of variation.

Step2: Calculate \(xy\) for each point

• For the point \((2,30)\): \(xy=2\times30 = 60\).
• For the point \((5,12)\): \(xy=5\times12=60\).
• For the point \((10,6)\): \(xy = 10\times6=60\).
• For the point \((30,2)\): \(xy=30\times2 = 60\).

Since for all the given points \((x,y)\) on the graph of the relationship between the side - lengths of the rectangle (where \(x\) represents width and \(y\) represents height), the product \(xy\) is a constant (\(k = 60\)).

Answer:

A. True