What is the area of the region bounded by stratight line 9 x + 4y = 36 , x - axis and the y - axis ?

Options

A. 12 sq. units
B. 18 sq. units
C. 16 sq. units
D. 15 sq. units

Answer

To find the area of the region bounded by the line \(9x + 4y = 36\), the x-axis, and the y-axis, we can follow these steps:

### Step 1: Find the x-intercept
To find the x-intercept, we set \(y = 0\) in the equation of the line.

\[ 9x + 4(0) = 36 \implies 9x = 36 \implies x = \frac{36}{9} = 4 \]

So, the x-intercept is at the point \((4, 0)\).

### Step 2: Find the y-intercept
To find the y-intercept, we set \(x = 0\) in the equation of the line.

\[ 9(0) + 4y = 36 \implies 4y = 36 \implies y = \frac{36}{4} = 9 \]

So, the y-intercept is at the point \((0, 9)\).

### Step 3: Sketch the triangle
The region bounded by the line, the x-axis, and the y-axis forms a right triangle with vertices at \((0, 0)\), \((4, 0)\), and \((0, 9)\).

### Step 4: Calculate the area of the triangle
The area \(A\) of a triangle can be calculated using the formula:

\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]

Here, the base is the length along the x-axis (from \((0, 0)\) to \((4, 0)\)), which is \(4\), and the height is the length along the y-axis (from \((0, 0)\) to \((0, 9)\)), which is \(9\).

Substituting the values into the area formula:

\[ A = \frac{1}{2} \times 4 \times 9 = \frac{36}{2} = 18 \]

Thus, the area of the region bounded by the line, the x-axis, and the y-axis is \(18\) square units.

### Final Answer:
The area of the region is \(18 \, \text{cm}^2\).

---