The dimensions of a square and equilateral triangle are shown below. if the difference between the area of the square and the perimeter of the triangle is equal to 3, what is a possible value of x?

a. -1/2
b. 1/4
c. 4
d. 8

A

Step-by-step explanation:

The area of a square is A = s². So the area of this square is A = (2x+2)² = 4x² + 8x + 4.

The perimeter of the triangle is 4/3x + 4/3x+4/3x = 12/3x = 4x.

The difference between the two values is subtraction. Subtract the expressions and simplify.

4x² + 8x + 4 -4x = 4x² + 4x + 4

This expression is also equal to 3. Set it equal to 3 and solve for x.

4x² + 4x + 4 = 3

4x² + 4x + 1 = 0

Substitute a = 4, b = 4 and c = 1 into the quadratic formula.

The quadratic formula is .

Substitute and you'll have:

you can't solve x because it is 2 linear equation and you only have one equation

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11