Question:
The park district is paying to enlarge the area of a square-shaped dock at a local lake. The area of the dock will increase by 16 square feet. Complete the equation below that can be used to find the area, x, of the original dock if the side length of the new dock is 20 feet.
So, the square root of what (?) equals(=) 20
Answer:
The complete equation is square root of(x + 16) = 20
Solution:
Given that Dock has a shape of square
[tex]\text{ area of square }= (side)^2[/tex]
From question, it is given that side length of new dock is 20 feet
Therefore, area of new dock is given as:
[tex]\text{ area of new dock}= (20)^2[/tex]
Taking square root on both sides,
square root of (new area ) = 20 --- eqn 1
Let "x" be the area of original dock
The area of the dock will increase by 16 square feet
New area = original area + 16
New area = x + 16 ---- eqn 2
From eqn 1,
square root of (new area ) = 20
From eqn 2
square root of(x + 16) = 20
Thus the complete equation is: square root of(x + 16) = 20
