The perimeter of a triangle is the sum of the lengths of its sides:

p = x + y + z
p = 5cm + 6cm + 14cm = 25cm

A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{1} \) = 1

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 1² + 1²
c² = 2
c = \( \sqrt{2} \)

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the < sign and the answer on the other.

-8x - 1 < -2 - 5x
-8x < -2 - 5x + 1
-8x + 5x < -2 + 1
-3x < -1
x < \( \frac{-1}{-3} \)
x < \(\frac{1}{3}\)

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

3b + 8 = \( \frac{b}{-4} \)
-4 x (3b + 8) = b
(-4 x 3b) + (-4 x 8) = b
-12b - 32 = b
-12b - 32 - b = 0
-12b - b = 32
-13b = 32
b = \( \frac{32}{-13} \)
b = -2\(\frac{6}{13}\)