a) Given
Total area = 81 feet squared.
Let the area of the square mat = x feet.
From question, area of the rectangular mat is twice that of square mat.
So, the area of the rectangular mat
feet.
Now,
Total area = 81 feet squared
Then,
![4(2 x) + x = 81\\ \\ 9 x = 81\\ \\ x = \frac{81}{9}\\ \\ x = 9\\](https://tex.z-dn.net/?f=4%282%20x%29%20%2B%20x%20%3D%2081%5C%5C%20%5C%5C%209%20x%20%3D%2081%5C%5C%20%5C%5C%20%20x%20%3D%20%5Cfrac%7B81%7D%7B9%7D%5C%5C%20%5C%5C%20x%20%3D%209%5C%5C)
Hence the area of the one rectangular mat = 2*9 = 18 feet squared
b) Let the width of the rectangular mat = y feet.
Then length of the mat = 2 y feet.
Area of the rectangle ![= 2 y* y = 2 y^{2}](https://tex.z-dn.net/?f=%3D%202%20y%2A%20y%20%3D%202%20y%5E%7B2%7D)
and area of rectangle = 18 feet squared.
So,
![2 y^{2} = 18\\ y^{2} = 9\\ y= \pm3\\](https://tex.z-dn.net/?f=2%20y%5E%7B2%7D%20%3D%2018%5C%5C%20y%5E%7B2%7D%20%3D%209%5C%5C%20y%3D%20%5Cpm3%5C%5C)
Width can not be negative.
Hence, the width of the rectangular mat = 3 feet
and length of the rectangular mat = 3*2 = 6 feet