Answer: s = 3n + 9 .
____________________________________________
Explanation:
____________________________________________
All squares are rectangles.
A square is a rectangle with 4 (FOUR) EQUAL side lengths.
A square has the same length and same length.
The formula for the area, "A", of a square is:
A = s² ; in which "s" is the side length of the square.
So, given: A = 9n² + 54n + 81 ; Find "s" ;
→ A = s² ;
↔ s² = A ;
Plug in our value given for "A" ;
→ s² = 9n² + 54n+ 81 ;
Take the positive square root of EACH SIDE of the equation; to isolate "s" on one side of the equation; & to solve for "s" (the side length);
Note: We take the "positive" square root" ; since the "side length of a square cannot be a "negative value" ;
→ √(s²) = √(9n² + 54n + 81) ;
Take the value under the square root sign:
"9n² + 54n + 81" ; and factor out a "9" ;
→ 9(n² +6n + 9)
And rewrite as:
√[9(n² + 6n + 9)] ;
____________________
Note: √[9(n² + 6n + 9)] = √9 * √(n² + 6n + 9) ;
√9 = 3 ;
√(n² + 6n + 9) is a perfect square; that is: √(n² + 6n + 9) = (n + 3 ) ;
So, √9 *√(n² + 6n + 9) = 3 * (n + 3) = 3*n + 3*3 = 3n + 9 ;
Rewrite:
√(s²) = 3n + 9 ;
____________________________________________
→ s = 3n + 9 .
____________________________________________
