Question

Tatami mats are used as a floor covering in japan. One possible layout uses four identical rectangular mats and one square mat, as shown. The area of the square mat is half the area of one of the rectangular mats.
a. Write and solve an equation to find the area a of one rectangular mat. Equation: =81 the area is ft2.
b. The length of a rectangular mat is twice the width. Use guess, check, and revise to find the dimensions on one rectangular mat. The length of the mat is feet and the width is feet. 5 of 7 answered check answer next

Answer 1

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 $= 2 x$ feet.

Now,

Total area = 81 feet squared

Then,

      $4(2 x) + x = 81\\ \\ 9 x = 81\\ \\ x = \frac{81}{9}\\ \\ x = 9$

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 $= 2 y* y = 2 y^{2}$

   and area of rectangle = 18 feet squared.

   So,

 $2 y^{2} = 18\\ y^{2} = 9\\ y= \pm3$

Width can not be negative.

Hence, the width of the rectangular mat = 3 feet

and  length of the rectangular mat = 3*2 = 6 feet