Answer:
The equation to determine the length is
.
The Length of the exercise mat is 16 feet.
Step-by-step explanation:
Given:
Perimeter of Rectangular mat = ![48\ ft](https://tex.z-dn.net/?f=48%5C%20ft)
Let the length of the mat be denoted by 'l'
And width be denoted by 'w'.
Also Given:
The length of the mat is twice the width of the mat.
So we can say that;
⇒ equation 1
Now we know that;
Perimeter of Rectangle is equal to twice the sum of length and width.
framing in equation form we get;
⇒ equation 2
Now Substituting equation 1 in equation 2 we get;
![2(2w+w)=48](https://tex.z-dn.net/?f=2%282w%2Bw%29%3D48)
Applying Distributive property we get;
![2\times2w+2\times w=48\\\\4w+2w=48](https://tex.z-dn.net/?f=2%5Ctimes2w%2B2%5Ctimes%20w%3D48%5C%5C%5C%5C4w%2B2w%3D48)
Hence, The equation to determine the length is
.
On Solving the above equation we get;
![4w+2w=48\\\\6w=48](https://tex.z-dn.net/?f=4w%2B2w%3D48%5C%5C%5C%5C6w%3D48)
Dividing both side by 6 we get;
![\frac{6w}{6}=\frac{48}{6}\\\\w=8\ ft](https://tex.z-dn.net/?f=%5Cfrac%7B6w%7D%7B6%7D%3D%5Cfrac%7B48%7D%7B6%7D%5C%5C%5C%5Cw%3D8%5C%20ft)
Now Substituting the value of 'w' in equation 1 we get;
![l=2w=2\times8=16\ ft](https://tex.z-dn.net/?f=l%3D2w%3D2%5Ctimes8%3D16%5C%20ft)
Hence The Length of the exercise mat is 16 feet.