A rectangular plot of land is 4x + 10 m long and 2x - 20 m wide. Its perimeter is 160 m. Calculate the value of x and the plot's dimensions.

Principal $(P) = \text{GH}\text{¢}36,000$
Annual interest rate $(R) = 12 \frac{1}{2}\% = 12.5\%$
Time $(T) = 6 \text{ months} = \frac{6}{12} \text{ years} = 0.5 \text{ years}$

The amount to be paid at the end of 6 months is $\boxed{\text{GH}\text{¢}38,250}$.

The monthly installment is $\boxed{\text{GH}\text{¢}6,375}$.

Given $P = 160\text{ m}$, $L = (4x + 10)\text{ m}$, $W = (2x - 20)\text{ m}$.

Divide both sides by 2:

Add 10 to both sides:

The value of $x$ is $\boxed{15}$.

The area of the plot is $\boxed{700 \text{ m}^2}$.

The total cost includes VAT.

Given Total Cost = GH¢4,830.00.

The actual cost of the machine is $\boxed{\text{GH}\text{¢}4,200}$.

The VAT paid on the machine is $\boxed{\text{GH}\text{¢}630}$.

The triangle PMN is a right-angled triangle with the right angle at M.
Side PM = $x + 1$
Side MN = 3
Hypotenuse PN = $x + 2$

Subtract $x^2$ from both sides:

Subtract $2x$ from both sides:

Subtract 4 from both sides:

The value of $x$ is $\boxed{3}$.

Find the sum of $(2\sqrt{5} - 4\sqrt{2})$ and $(3\sqrt{5} + 5\sqrt{2})$.

The sum is $\boxed{5\sqrt{5} + \sqrt{2}}$.