Question

SQUARES The area of a square y can be modeled by the function y = x², where x is

the side length of the square. The perimeter of a square can be modeled by the
function y = 4x.
a. Solve the system of equations algebraically.
b. If the area of a square in square units is equal to the perimeter of the square in
units, what is the side length of the square? What are the area and perimeter of
the square?

Answer 1

a. To solve the system of equations algebraically:

y = x² (equation 1)
y = 4x (equation 2)

Substituting equation 1 into equation 2, we get:

x² = 4x

Rearranging and factoring, we get:

x(x - 4) = 0

Therefore, x = 0 or x = 4. However, a square cannot have a side length of 0, so the only solution that makes sense is x = 4.

Substituting x = 4 into equation 1, we get:

y = 4² = 16

Therefore, the side length of the square is 4 units, the area of the square is 16 square units, and the perimeter of the square is 4x4 = 16 units.

b. If the area of the square is equal to its perimeter, then we can set the two equations equal to each other:

x² = 4x

Rearranging and factoring, we get:

x(x - 4) = 0

Therefore, x = 0 or x = 4. However, a square cannot have a side length of 0, so the only solution that makes sense is x = 4.

Therefore, the side length of the square is 4 units, the area of the square is 16 square units, and the perimeter of the square is 4x4 = 16 units.