Question

a rectangle has a width of 3/4 inches and a length of 9/10 inches. anoth larger but still proportional to the first rectangle. it has a width of 30 i length of 36 inches. what proportion could model this situation? a) 3/4 divided by 9/10 = 36/30 b) 3/4 divided by 9/10 = 30/36 c) 9/10 divided by 3/4 = 30/36 d) 36/3 = 30/9

Explanation:

Step1: Recall the property of proportional rectangles

For two proportional rectangles, the ratio of width to length of the first rectangle is equal to the ratio of width to length of the second rectangle.
The first rectangle has width \(w_1=\frac{3}{4}\) and length \(l_1 = \frac{9}{10}\). The second rectangle has width \(w_2 = 30\) and length \(l_2=36\). So the proportion should be \(\frac{w_1}{l_1}=\frac{w_2}{l_2}\)

Step2: Substitute the values into the proportion formula

Substitute \(w_1=\frac{3}{4}\), \(l_1=\frac{9}{10}\), \(w_2 = 30\), and \(l_2 = 36\) into \(\frac{w_1}{l_1}=\frac{w_2}{l_2}\), we get \(\frac{\frac{3}{4}}{\frac{9}{10}}=\frac{30}{36}\)

Answer:

B. \(\frac{\frac{3}{4}}{\frac{9}{10}}=\frac{30}{36}\)