QUESTION 1
The perimeter of the mat is given to be [tex]36\:ft.[/tex]
Let the width of the mat be [tex]w\:ft[/tex]
Then [tex]l=2w...(1)\:ft[/tex]
The formula for finding the perimeter is;
[tex]p=2w+2l...(2)[/tex]
We substitute the given value of the perimeter and equation (1) into equation (2) to obtain;
[tex]36=2w+2(2w)[/tex]
[tex]\Rightarrow 36=2w+4w[/tex]
[tex]\Rightarrow 36=6w[/tex]
[tex]\Rightarrow 6=w[/tex]
QUESTION 2
The length of the rectangular exercise mat is;
[tex]l=2(6)\:ft[/tex]
[tex]l=12\:ft[/tex]
The area of the rectangular mat can be found using the formula;
[tex]A=l\times w[/tex]
We substitute the values to obtain;
[tex]Area=12\times 6\:ft^2[/tex]
[tex]Area=72\:ft^2[/tex].
The area of the given rectangular mat is; 72 ft²
We are given;
Perimeter of Rectangle; P = 36 ft
Length; L = 2w
Formula for perimeter of rectangle is;
P = 2L + 2w
P = 2(2w) + 2w
P = 6w
6w = 36
w = 36/6
w = 6 ft
L = 2w = 2(6)
L = 12 ft
Area of rectangle mat = 12 * 6 = 72 ft²
Read more about Area of a rectangle at; https://brainly.com/question/13048427
