Answer:
The company's largest rug dimensions are either 18 ft by 27 ft Or 12 ft by 18 ft.
Step-by-step explanation:
Given:
Dimension of the smaller rug are 2 ft by 3 ft.
Also One side of the largest rug is 18 ft.
We need to find the possible dimension of largest rug.
Also Given:
Both the smaller rug and larger rugs are similar.
Now By Similar rectangles property which states that;
"When 2 rectangles are similar then their lengths are in proportion."
In this case there are 2 possibilities.
either the largest rug's 18 ft side is similar to the 2 ft side or the 3 ft side
Now let us consider the other side be 'x'.
Now when he largest rug's 18 ft side is similar to the 2 ft side we get;
[tex]\frac{2}{3}=\frac{18}{x}\\\\x=18\times\frac{3}{2} = 27\ ft[/tex]
Now when he largest rug's 18 ft side is similar to the 3 ft side we get;
[tex]\frac{2}{3}=\frac{x}{18}\\\\x=\frac{2}{3}\times 18 = 12\ ft[/tex]
Hence the company's largest rug dimensions are either 18 ft by 27 ft OR 12 ft by 18 ft.
