A meteorologist is studying the monthly rainfall in a section of the Brazilian rainforest. She recorded the monthly rainfall, in
2 answers:
You might be interested in
Answer:
Part A)
Part B)
Approximately 18.77 feet long by 20.77 feet wide.
Step-by-step explanation:
Currently, the patio is 13 feet long by 15 feet wide. Therefore, the area right now is:
We will increase the length and width of the patio by the same amount such that the new area is double the previous amount.
Part 1)
The previous area is 195. Therefore, we would like to the new area to be twice of that. Hence, the new area is:
We will increase the length and the width by the same amount. Let’s call this amount x. Then by the area formula (A=bh), we can write:
390 represents the doubled area. (15+x) is the width after the increase x, and (13+x) is the length after the same x increment.
Part 2)
So, we will solve for x. First, expand:
Simplify:
Subtract 390 from both sides:
This is a quadratic. Hence, we can use the quadratic formula:
Our a=1, b=28, and c=-195. Hence:
Evaluate:
Simplify the square root:
Hence:
Simplify:
Approximate:
In this case, we can reject the negative solution.
Hence, the value of x is 5.77.
This means that we should increase the our length and width by 5.77.
Hence, the new length will be 13+5.77 or about 18.77.
And our new width will be 15+5.77 or about 20.77.
So, the new dimensions is approximately 18.77 by 20.77