Question

A rectangle or exercise mat has a perimeter of 48 feet the length of the mat Is twice The lift right and solve any questions to determine the length in feet of the mat

Answer 1

Answer:

The equation to determine the length is $4w+2w=48$.

The Length of the exercise mat is 16 feet.

Step-by-step explanation:

Given:

Perimeter of Rectangular mat = $48\ ft$

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;

$l=2w$  ⇒ 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;

$2(l+w)=48$ ⇒ equation 2

Now Substituting equation 1 in equation 2 we get;

$2(2w+w)=48$

Applying Distributive property we get;

$2\times2w+2\times w=48\\\\4w+2w=48$

Hence, The equation to determine the length is $4w+2w=48$.

On Solving the above equation we get;

$4w+2w=48\\\\6w=48$

Dividing both side by 6 we get;

$\frac{6w}{6}=\frac{48}{6}\\\\w=8\ ft$

Now Substituting the value of 'w' in equation 1 we get;

$l=2w=2\times8=16\ ft$

Hence The Length of the exercise mat is 16 feet.