Question

a 4-foot long rectangle of fabric costs $16.50. assuming the price per square is constant, what is the cost of a similar rectangle of fabric that is 24 feet long?

Answer 1

For this problem, we are told the price of a 4-foot long rectangle fabric. If we assume that a similar rectangle of fabric is 24 feet long, we need to calculate its cost.

The area for a rectangle is given below:

$A=\text{ length}\cdot\text{ width}$

For two rectangles to be simillar, their dimensions must be related by a constant ratio. Therefore we have:

$r=\frac{24}{4}=6$

Which means that each side is increased by a ratio of 6 from the original rectangle. The second rectangle must be:

$\begin{gathered} A_1=4\cdot\text{ width1}\\ \\ A_2=6\cdot4\cdot6\cdot\text{ width2}\\ \\ A_2=36\cdot4\cdot\text{ width2}\\ \\ A_2=36\cdot A_1 \end{gathered}$

The area of the second rectangle is 36 times the one of the first. Therefore the price should be 36 times as well. We have:

$\text{ Cost }=36\cdot16.5=594$

The cost of the second one will be $594.