Answer:
1) The equation that represents the total area of Riley's proposed ratio is .
2) The length and width of the new patio are approximately 18.4 feet and 21.2 feet, respectively.
Step-by-step explanation:
1) From Geometry we remember that area formula for the rectangle is represented by:
(1)
Where:
- Area, measured in square feet.
- Length, measured in feet.
- Width, measured in feet.
From statement we know that Riley wants to double the area, that is:
(2)
By applying (1) in (2), we get the following expression:
(3)
Given that Riley wants to double the area of the pation by increasing the length and width by the same amount, we can rearrange (3) by algebraic means:
(3b)
The equation that represents the total area of Riley's proposed ratio is .
2) If we know that and
, then the length and the width of the new patio are, respectively:
The length and width of the new patio are approximately 18.4 feet and 21.2 feet, respectively.