A rectangular courtyard has an area of 40 sq m. Its length is (x+2) m and its width is (x-4) m. Find its dimensions.

Let the length of the courtyard be $L$ meters.
Let the width of the courtyard be $W$ meters.
Given: $L = (x+2)$ m and $W = (x-4)$ m.

The area of a rectangle is $A = L \times W$.
Given $A = 40 \text{ m}^2$.

Rearrange into a standard quadratic form:

We need two numbers that multiply to -48 and add to -2. These numbers are -8 and 6.

Set each factor to zero:

Since dimensions (length and width) cannot be negative, $x$ must be positive. If $x=-6$, the width $(x-4)$ would be $-10$, which is not possible. Therefore, $x=8$.

Length $L = (x+2) = (8+2) = 10$ m.
Width $W = (x-4) = (8-4) = 4$ m.

The length of the courtyard is $\boxed{\text{10 m}}$ and the width is $\boxed{\text{4 m}}$.

Let $x$ be the original number of women in the group.
The total amount to be contributed is sh 1200.
The original contribution per woman would be $\frac{1200}{x}$ shillings.

Five women were unable to contribute, so the new number of women is $x-5$.
The remaining women contributed sh 20 more than the original amount per woman.
So, the new contribution per woman is $\left(\frac{1200}{x} + 20\right)$ shillings.

The total amount contributed by the remaining women is still sh 1200.
(New number of women) $\times$ (New contribution per woman) = Total amount

Subtract 1200 from both sides:

The quadratic equation representing the information is $\boxed{x^2 - 5x - 300 = 0}$.