Explanation:

- We know the formula for the area of a triangle is $\frac{1}{2}\times \text{base}\times \text{height}$.

- Given the height is 24 cm, we can calculate the base as follows:

$$

168 = \frac{1}{2} \times \text{base} \times 24

$$

Solving for base:

$$

\text{base} = \frac{168 \times 2}{24} = 14 \, \text{cm}

$$

- The base of the triangle is equal to the breadth of the rectangle, so the rectangle's breadth is 14 cm.

- The perimeter of the rectangle is 84 cm, and the formula for the perimeter is $2\times (\text{length}+\text{breadth})$.

- Thus:

$$

84 = 2 \times (\text{length} + 14)

$$

Solving for length:

$$

84 = 2 \times (\text{length} + 14) \implies 42 = \text{length} + 14 \implies \text{length} = 28 \, \text{cm}

$$

- Option 3: 28 cm is correct.