Question

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

Answer 1

Answer:

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 $x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}$.

Substitute and you'll have:

$x=\frac{-b+/-\sqrt{b^2-4ac} }{2a} =\frac{-4+/-\sqrt{4^2-4(4)(1)} }{2(4)}=\frac{-4+/-\sqrt{16-16} }{8)}$

$\frac{-4+/-\sqrt{0} }{8} = \frac{-4}{8}=\frac{-1}{2}$