We know that a medical supplier sells gauze in large and small rectangular sheets. Consider the given information about each type of sheet.
A large sheet has a length of 9 inches and an area of 45 square inches.
A small sheet has a length of 4 inches and a width of 3 inches.
We want to know if the sheets are similar. To do so, let's start by recalling the formula for the area of a rectangle.
A= l * w
Here, l indicates the length of the rectangle and w the width. Let's start by finding the width of the larger sheet. We will substitute l= 9 and A= 45 into the formula for the area and solve for w.
The width of the larger sheet is equal to 5 inches. Now that we have all the information about the side lengths of both sheets, we can use a condition for similarity to see if they are similar figures. To do so, we will write a proportion between the corresponding side lengths.
l_1/l_2= w_1/w_2
Here, the subscript 1 represents the larger sheet and the subscript 2 represents the smaller sheet. This condition must be true if the sheets are similar. Let's substitute the known values into the equation to see if the sheets are similar.
9/4≠5/3
Therefore, the rectangular sheets are not similar because the corresponding sides lengths are not proportional.
