Question

3- a rectangular garden has a length of 16m and a width of 9m.
(a) calculate the area of the garden.
(b) if the length is increased by 25%, what is the new area of the garden?

4- a farmer harvested 1200 kg of maize. if he sold \\(\frac{1}{5}\\) of it, how much maize did he sell and how much remained?

Explanation:

Problem 3:

Part (a)

Step 1: Recall the formula for the area of a rectangle

The area \( A \) of a rectangle is given by the formula \( A = \text{length} \times \text{width} \).

Step 2: Substitute the given values

Given length \( l = 16 \, \text{m} \) and width \( w = 9 \, \text{m} \). Substituting these values into the formula, we get \( A = 16 \times 9 \).

Step 3: Calculate the product

\( 16 \times 9 = 144 \).

Step 1: Find the new length after a 25% increase

First, calculate 25% of the original length. 25% of \( 16 \) is \( 0.25 \times 16 = 4 \). Then, the new length \( l_{\text{new}} = 16 + 4 = 20 \, \text{m} \).

Step 2: Calculate the new area

Using the area formula for a rectangle \( A = \text{length} \times \text{width} \), with the new length \( l_{\text{new}} = 20 \, \text{m} \) and width \( w = 9 \, \text{m} \), we get \( A_{\text{new}} = 20 \times 9 \).

Step 3: Calculate the product

\( 20 \times 9 = 180 \).

Step 1: Calculate the amount of maize sold

The farmer sold \( \frac{1}{5} \) of \( 1200 \, \text{kg} \). To find this, we calculate \( \frac{1}{5} \times 1200 \).

Step 2: Simplify the calculation

\( \frac{1}{5} \times 1200 = \frac{1200}{5} = 240 \, \text{kg} \).

Step 3: Calculate the amount of maize remaining

Subtract the amount sold from the total amount. So, remaining maize \( = 1200 - 240 \).

Step 4: Calculate the difference

\( 1200 - 240 = 960 \, \text{kg} \).

Answer:

The area of the garden is \( 144 \, \text{m}^2 \).

Part (b)