A cube is a rectangular solid box with a height (h), length (l), and width (w). The volume is h x l x w and the surface area is 2lw x 2wh + 2lh.

The surface area of a cube is (2 x length x width) + (2 x width x height) + (2 x length x height):

sa = 2lw + 2wh + 2lh
sa = (2 x 4 x 2) + (2 x 2 x 9) + (2 x 4 x 9)
sa = (16) + (36) + (72)
sa = 124

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 = \( \sqrt{a} \) = \( \sqrt{4} \) = 2

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 = 2² + 2²
c² = 8
c = \( \sqrt{8} \) = \( \sqrt{4 x 2} \) = \( \sqrt{4} \) \( \sqrt{2} \)
c = 2\( \sqrt{2} \)

You need to find the value of c so solve the first equation in terms of y:

3c + y = -8
y = -8 - 3c

then substitute the result (-8 - 3c) into the second equation:

-9c - 5(-8 - 3c) = -3
-9c + (-5 x -8) + (-5 x -3c) = -3
-9c + 40 + 15c = -3
-9c + 15c = -3 - 40
6c = -43
c = \( \frac{-43}{6} \)
c = -7\(\frac{1}{6}\)

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

p = x + y + z
p = 11cm + 14cm + 6cm = 31cm