Question

Please help me find out what k is.

Answer 1

Answer: a) k=8

b) The area of the addition =$30\text{ square feet}$

The area of the entire patio after addition $=80\ \text{square feet}$

Step-by-step explanation:

Given: The area of the patio before addition = 50 square feet

The area of the addition portion is given by $k^2-3k-10$

We can see that dimension of the total portion is $k\times(k+2)$

therefore, the area of the patio with the addition portion = $k\times(k+2)=k^2+2k$

According to the question we have,

$k^2-3k-10+50=k^2+2k\\\Rightarrow-3k+40=2k\\\Rightarrow\ 5k=40\\\Rightarrow\ k=8$

Therefore,  The area of the addition =$8^2-3(8)-10=64-24-10=30\text{ square feet}$

The area of the entire patio after addition =  $30+50=80\ \text{square feet}$