Opposite angles are equal, and adjacent angles must sum to 180.

Therefore, we can set up an equation to solve for z:

(z – 15) + 2z = 180

3z - 15 = 180

3z = 195

z = 65

Now solve for x:

2z = x = 130°

To solve this question you must know the formula for the area of a parallelogram.

In this equation, \(\displaystyle B\) is the length of the base and \(\displaystyle H\) is the length of the height. We can plug in the side length for both base and height, as given in the question.

\(\displaystyle A=8*7\)

\(\displaystyle A=56\)

To solve this question you must know the formula for the area of a parallelogram.

The formula is 

So we can plug in the side length for both base and height to yield \(\displaystyle A=12*8\)

Perform the multiplication to arrive at the answer of \(\displaystyle A=96\).

The formula for the area of a parallelogram is:

\(\displaystyle A=(b)(h)\),

where \(\displaystyle b\) is the length of the base and \(\displaystyle h\) is the length of the height.

In order to the find the height of the parallelogram, use the formula for a \(\displaystyle 30-60-90\) triangle:

\(\displaystyle a-a\sqrt{3}-2a\), where \(\displaystyle a\) is the side opposite the \(\displaystyle \measuredangle30\).

The left side of the parallelogram forms the following \(\displaystyle 30-60-90\) triangle:

\(\displaystyle 4m-4\sqrt{3}m-8m\), where \(\displaystyle 4\sqrt{3}m\) is the length of the height.

Plugging in our values, we get:

\(\displaystyle A=(12m)(4\sqrt{3}m)=48\sqrt{3}m^2\)

Use the Pythagorean Theorem to determine the length of the diagonal:

\(\displaystyle A^2 + B^2 = C^2\)

\(\displaystyle (9m)^2 + B^2 = (16m^2)\)

\(\displaystyle B^2 = 175m^2\)

\(\displaystyle B = 5 \sqrt{7}m\)

The area of the parallelogram is twice the area of the right triangles:

\(\displaystyle A_{Triangle} = \frac{1}{2} (b)(h)\)

\(\displaystyle A_{Triangle} = \frac{1}{2} (9m)(5m\sqrt{7}) = \frac{45m^2\sqrt{7}}{2}\)

\(\displaystyle A_{Parallelogram} = 2 (A_{Triangle}) = 2\left(\frac{45m^2\sqrt{7}}{2}\right)=45m^2\sqrt{7}\)

The formula for the area of a parallelogram is

\(\displaystyle A = (base)(height)\).

Use the formula for a \(\displaystyle 45-45-90\) triangle to find the length of the height:

\(\displaystyle a-a-a\sqrt{2}\)

\(\displaystyle 4\ m-4\ m-4\sqrt{2}\ m\)

Plugging in our values, we get:

\(\displaystyle A = (19\ m)(4\ m)\)

\(\displaystyle A = 760\ m^2\)

Solve for the height of the second rectangle.

Perimeter = 2B + 2H

12 = 2(4) + 2H

12 = 8 + 2H

4 = 2H

H = 2

If they are similar, then the base and height are proportionally equal.

B₁/H₁ = B₂/H₂

4/2 = B₂/H₂

2 = B₂/H₂

B₂ = 2H₂

Use perimeter equation then solve for H:

Perimeter = 2B + 2H

36 = 2 B₂ + 2 H₂

36 = 2 (2H₂) + 2 H₂

36 = 4H₂ + 2 H₂

36 = 6H₂

H₂ = 6

Given that w = 2x and l = 1.5w + 5, a substitution will show that l = 1.5(2x) + 5 = 3x + 5.  

P = 2w + 2l = 2(2x) + 2(3x + 5) = 4x + 6x + 10 = 10x + 10 = 10(x + 1)

The perimeter of a figure is the sum of the lengths of all of its sides. The perimeter of this figure is √27 + 2√3 + √27 + 2√3. But, √27 = √9√3 = 3√3 . Now all of the sides have the same number underneath of the radical symbol (i.e. the same radicand) and so the coefficients of each radical can be added together. The result is that the perimeter is equal to 10√3.

Divide the area of the rectangle by the width in order to find the length of 14 feet. The perimeter is the sum of the side lengths, which in this case is 14 feet + 4 feet +14 feet + 4 feet, or 36 feet.