We know that this piece of fabric costs $1.31. We want to find the total cost of a similar piece of fabric that is 18 inches by 42 inches. Notice that the side lengths of the new piece of fabric are twice the side lengths of the old piece of fabric. This means that the ratio between the corresponding side lengths is 2.
New piece of fabric/Old piece of fabric=42/21 =2
Remember that when two figures are similar, the value of the ratio of their areas is equal to the square of the value of the ratio of their corresponding side lengths.
New area/Old area=2^2=4
We found that the area of the new piece of fabric is 4 times the area of the old piece of fabric. This means that the cost of the new piece of fabric will be 4 times the cost of the old piece of fabric.
4($ 1.31)=$ 5.24
Therefore, the new piece of fabric costs $5.24.
