Answer: a) k=8
b) The area of the addition =[tex]30\text{ square feet}[/tex]
The area of the entire patio after addition [tex]=80\ \text{square feet}[/tex]
Step-by-step explanation:
Given: The area of the patio before addition = 50 square feet
The area of the addition portion is given by [tex]k^2-3k-10[/tex]
We can see that dimension of the total portion is [tex]k\times(k+2)[/tex]
therefore, the area of the patio with the addition portion = [tex]k\times(k+2)=k^2+2k[/tex]
According to the question we have,
[tex]k^2-3k-10+50=k^2+2k\\\Rightarrow-3k+40=2k\\\Rightarrow\ 5k=40\\\Rightarrow\ k=8[/tex]
Therefore, The area of the addition =[tex]8^2-3(8)-10=64-24-10=30\text{ square feet}[/tex]
The area of the entire patio after addition = [tex]30+50=80\ \text{square feet}[/tex]
