Question

The area of the triangle formed by the lines $\mathrm{x}=0$, $\mathrm{y}=0$ and $\frac{\mathrm{x}}{\mathrm{a}}+\frac{\mathrm{y}}{\mathrm{b}}=1$ is

• A. $\mathrm{ab}$
• B. $\frac{\mathrm{ab}}{2}$
• C. $2\mathrm{ab}$
• D. $\frac{\mathrm{ab}}{3}$

Answer 1

The correct option is B

$\frac{\mathrm{ab}}{2}$

Explanation for correct option

Calculating the area of the triangle

Given,

The lines $\mathrm{x}=0$ and $\mathrm{y}=0$ are y-axis and x-axis respectively. They meet at $\left(0,0\right)$.

The 3rd line is $\frac{\mathrm{x}}{\mathrm{a}}+\frac{\mathrm{y}}{\mathrm{b}}=1$ . Here the x-intercept is $\mathrm{a}$ and the y-intercept is $\mathrm{b}$.

We understand that the x-axis and y-axis will act as the base and height of the triangle and the third line will act as the hypotenuse. Also, the base of the triangle will be nothing but the x-intercept and the height will be the y-intercept.

So, the coordinates of the required triangle is $(0,0),\left(\mathrm{a},0\right),\left(0,\mathrm{b}\right)$.

Therefore, the area of the required triangle is given by,

$$\begin{gathered} \mathrm{Area}=\frac{1}{2}\times \mathrm{base}\times \mathrm{height} \\ =\frac{1}{2}\times \mathrm{x}-\mathrm{intercept}\times \mathrm{y}-\mathrm{intercept} \\ =\frac{1}{2}\times \mathrm{ab} \end{gathered}$$

Hence, the correct answer is Option (B).