ANSWER TO QUESTION 1
Let the width be
![w](https://tex.z-dn.net/?f=w)
units.
Twice the width will be
![2w](https://tex.z-dn.net/?f=2w)
Two more than twice the width will be
![2w + 2](https://tex.z-dn.net/?f=2w%20%2B%202)
We were told that the length is 2 more than twice the width. This means that,
![l = 2w + 2](https://tex.z-dn.net/?f=l%20%3D%202w%20%2B%202)
This implies that,
![w = \frac{l - 2}{2} - - eqn(1)](https://tex.z-dn.net/?f=w%20%3D%20%20%5Cfrac%7Bl%20-%202%7D%7B2%7D%20%20-%20%20-%20eqn%281%29)
The formula for finding the perimeter of a rectangle is given by:
![perimeter = 2w + 2l - - eqn(2)](https://tex.z-dn.net/?f=perimeter%20%3D%202w%20%2B%202l%20-%20%20-%20eqn%282%29)
We substitute 124 for the perimeter and equation (1) into equation (2)
![124 = 2( \frac{l - 2}{2} ) + 2l](https://tex.z-dn.net/?f=124%20%3D%202%28%20%5Cfrac%7Bl%20-%202%7D%7B2%7D%20%29%20%2B%202l)
This implies that,
![124 = l - 2 + 2l](https://tex.z-dn.net/?f=124%20%3D%20l%20-%202%20%2B%202l)
![\Rightarrow 124 + 2 = l + 2l](https://tex.z-dn.net/?f=%5CRightarrow%20124%20%2B%202%20%3D%20l%20%2B%202l)
![\Rightarrow 126 = 3l](https://tex.z-dn.net/?f=%5CRightarrow%20126%20%3D%203l)
We divide both sides by 3 to obtain,
![l = 42](https://tex.z-dn.net/?f=l%20%3D%2042)
Therefore the length is 42 feet.
ANSWER TO QUESTION 2
Let the width be
![w](https://tex.z-dn.net/?f=w)
units.
Five more than the width will be
![w + 5](https://tex.z-dn.net/?f=w%20%2B%205)
We were told that the length is 5 more than the width. This means that,
![l = w + 5](https://tex.z-dn.net/?f=l%20%3D%20w%20%2B%205)
We make w the subject to obtain,
![w = l - 5 - - eqn(1)](https://tex.z-dn.net/?f=w%20%3D%20l%20-%205%20-%20%20-%20eqn%281%29)
The perimeter is given by,
![perimeter = 2w + 2l - - eqn(2)](https://tex.z-dn.net/?f=perimeter%20%3D%202w%20%2B%202l%20-%20%20-%20eqn%282%29)
We substitute 50 for the perimeter and equation (1) into equation (2)
![50 = 2(l - 5) + 2l](https://tex.z-dn.net/?f=50%20%3D%202%28l%20-%205%29%20%20%2B%202l)
Dividing through by 2 gives,
![25 = l - 5 + l](https://tex.z-dn.net/?f=25%20%3D%20l%20-%205%20%2B%20l)
![\Rightarrow 25 + 5 = l + l](https://tex.z-dn.net/?f=%5CRightarrow%2025%20%2B%205%20%3D%20l%20%2B%20l)
![\Rightarrow 30 = 2l](https://tex.z-dn.net/?f=%5CRightarrow%2030%20%3D%202l)
We divide both sides by 2 to get,
![l = 15](https://tex.z-dn.net/?f=l%20%3D%2015)
Therefore the length is 15 feet.