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 exhibit inverse variation, the relationship is \(y=\frac{k}{x}\) or \(xy = k\) (where \(k\) is a non - zero constant).

Step2: Check the product of \(x\) (width) and \(y\) (height) for each point

• For the point \((4,25)\): \(4\times25=100\)
• For the point \((5,20)\): \(5\times20 = 100\)
• For the point \((10,10)\): \(10\times10=100\)
• For the point \((20,5)\): \(20\times5=100\)

Since for each pair of values (width \(x\) and height \(y\)) in the graph, the product \(xy\) is a constant (\(k = 100\)), the adjacent side lengths (width and height) of the rectangle exhibit inverse variation.

Answer:

A. True