Answer:
Length of mat = 4 inches
Width of mat = 12 inches
Area of table mat = 48 square inches
Step-by-step explanation:
Given
Perimeter = P = 32
Let l be the length of the table mat and w be the width of table mat
According to given statement
[tex]w = 3l[/tex]
The perimeter of a rectangular object is given by:
[tex]P = 2(l+w)[/tex]
Putting w=3l and value of P
[tex]32 = 2(l+3l)\\2(4l) = 32\\8l = 32[/tex]
Dividing both sides by 8
[tex]\frac{8l}{8} = \frac{32}{8}\\l = 4[/tex]
So
Length = l = 4 inches
And
Width = 3l = 3*4 = 12
Now
[tex]Area = l * w\\A = 4 * 12\\A = 48\ in^2[/tex]
Hence,
Length of mat = 4 inches
Width of mat = 12 inches
Area of table mat = 48 square inches
