Question

a company makes rugs. their smallest rug is a 2 ft-by-3 ft rectangle. their largest rug is a similar rectangle. if one side of their largest rug is 18 ft, what are the possible dimensions of their largest rug? there are two possible sets dimensions. list the two sets below. the smallest dimension is listed first.

Answer 1

The company's largest rug dimensions are either 18 ft by 27 ft Or 12 ft by 18 ft.

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;

Now when he largest rug's 18 ft side is similar to the 3 ft side we get;

Hence the company's largest rug dimensions are either 18 ft by 27 ft OR 12 ft by 18 ft.