Question

39 multiple choice 2 points
does the ratio of the lengths of the sides of a rectangle that is 48 in. by 64 in. match the golden ratio?
no, because they cannot be cut into a square and a smaller rectangle.
yes, because both sides are divisible by 8.
no, because the ratio of the sides is not the same as the ratio of their sum to the larger side.
yes, because it is a euclidean shape.

Explanation:

Step1: Calculate the ratio of the sides

The ratio of the sides of the rectangle is \(\frac{48}{64}=\frac{3}{4} = 0.75\)

Step2: Recall the property of the Golden Ratio

For the Golden Ratio \(\frac{a}{b}=\frac{a + b}{a}\) (where \(a>b>0\)). Let \(a = 64\) and \(b=48\). The ratio of their sum to the larger side is \(\frac{48 + 64}{64}=\frac{112}{64}=\frac{7}{4}=1.75\). Since \(0.75
eq1.75\)

Answer:

C. No, because the ratio of the sides is not the same as the ratio of their sum to the larger side.