A square has a side of x + 13. the area of the square is 441. Find x

Question

find the area of the square 

Answer 1

 

Area of square is a side squared. 

 

       (x + 13)(x + 13) = 441

       (x + 13)² = 441

 

Take the square root of both sides

 

        x + 13 = √(441)

 

Solve for x

 

         x = 21 - 13

         x = 8

 

The sides of the square are 8 + 13 = 21

The area is 21•21 = 441

Answer 2

1. Area of a Square=(Side)²

2. Plug in known information: 441=(x+13)²

3. Solve for x:

Option a (expand and use quadratic formula):

441=x²+26x+169

0=x²+26x-272

Use quadratic formula to solve for x

Option b:

Take the square root of both sides to obtain:

+/-(441^1/2)=x+13

Thus, x=+/-(441^1/2)-13

Since negative distance is incoherent, we can ignore the negative result as extraneous.

Simplification yields x=8.

 

 

Answer 3

This question requires that you understand that all sides of a square have the same length, and that the area is the length of any side squared.   So if one side is (x+13), then all sides of the square are (x+13) and the area is (x+13)².   

 

(x+13)² = 441

 

(x+13)2 = 21²

 

If we take the square root of both sides, and take into account double solutions.

 

X+13 = +/- 21;

 

X = -13 +/- 21;   x = 8 or -33.   Since only the value of x that makes (x+13) positive has a real meaning, then x is 8.