Question

Tatami mats are used as a floor covering in Japan. one possible layout uses four identical rectangular mats and one square mat. The area of the square mat is half the area of one of the rectangular mats. What is the length and width of one rectangular mat?

Answer 1

Answer with explanation:

→  Let L be the Length and B be the Breadth of rectangular mat.

     Area of rectangular Mat = Length (L) * Breadth (B)

                                              =L*B square units

→  Let , a be the side of Square.

Area of square =(Side)²

                             =a² square units

→→It is also, given that The area of the square mat is half the area of one of the rectangular mats.

$\rightarrow a^2=\frac{LB}{2}\\\\LB=2a^2\\\\ \text{Length of one square mat(L)}=\frac{2a^2}{\text{Breadth(B)}}\\\\\L=\frac{2\times {\text{Area of Square}}}{\text{Breadth of rectangle}}\\\\B=\frac{2\times {\text{Area of Square}}}{\text{Length of rectangle}}$

Answer 2

So by definition, area is equal to the length (x) times the width (y). The area of the square mat is = x × y, or xy
If the area of the rectangular mat is twice that of the square mat, the area of the rectangular mat would have to be = 2 × x × y
This can be written as 2x × y, making the length of the rectangular mat twice that of the square mat's length, and the width the same as the square mat's width.