Respuesta :
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 [tex]= 2 x[/tex] feet.
Now,
Total area = 81 feet squared
Then,
[tex]4(2 x) + x = 81\\ \\ 9 x = 81\\ \\ x = \frac{81}{9}\\ \\ x = 9\\[/tex]
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 [tex]= 2 y* y = 2 y^{2}[/tex]
and area of rectangle = 18 feet squared.
So,
[tex]2 y^{2} = 18\\ y^{2} = 9\\ y= \pm3\\[/tex]
Width can not be negative.
Hence, the width of the rectangular mat = 3 feet
and length of the rectangular mat = 3*2 = 6 feet
The area of one rectangular portion of the tatami mat is 18ft².
The dimension of the one rectangular portion of the tatami mat is ;width = 3ft and length = 6ft
Total area of mat = 81 ft²
Mat layout = (4 identical rectangular mat + 1 square mat)
Area of square mat = 1/2 × (Area of one rectangular mat)
Let :
area of square mat = x
Area of rectangular mat = 2x
Total area could be expressed as :
[Area of square mat + (4 × area of rectangular mat)] = 81 ft²
Total area of tatami mat :
[x + 4(2x)] ft² = 81 ft²
[x + 8x] = 81ft²
9x = 81
x = 81/9
x = 9
Recall:
Area of one rectanglular mat = 2x
Area of one rectanglular mat = 2(9) = 18ft²
B)
Length of one rectangular mat is twice the width
If :
Width = a
Then ;
Length = 2a
Formula for area of rectangle :
Area = Length × width
18 = a × 2a
18 = 2a²
a² = 18/2
a² = 9
a = √9
a = 3
Width of one rectangle = a = 3ft
Length of one rectangle = 2a = 2(3) = 6ft
Hence, one rectangular area of the tatami mat is 18ft² ; with rectangular dimension of 6ft by 3ft.
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