Question

The area enclosed by the pair of lines $xy=0$, the line $x-4=0$ and $y+5=0$ is

• A. $20\mathrm{sq}.\mathrm{units}$
• B. $10\mathrm{sq}.\mathrm{units}$
• C. $\frac{5}{4}\mathrm{sq}.\mathrm{units}$
• D. $0\mathrm{sq}.\mathrm{units}$

Answer 1

The correct option is A

$20\mathrm{sq}.\mathrm{units}$

Explanation for correct option

Given pair of lines are $xy=0$ which implies that, $x=0$ and $y=0$

Also,

$$\begin{gathered} x-4=0 \\ \Rightarrow x=4 \end{gathered}$$

Similarly,

$$\begin{gathered} y+5=0 \\ \Rightarrow y=-5 \end{gathered}$$

The graph formed by these lines is as shown:

Therefore it is a rectangle with length $5\mathrm{units}$ and breadth $4\mathrm{units}$. Therefore the required area is,

$$\begin{gathered} \mathrm{Area}=\mathrm{length}\times \mathrm{breadth} \\ =5\times 4 \\ =20\mathrm{square}\mathrm{units} \end{gathered}$$

So the area enclosed is equal to $20\mathrm{square}\mathrm{units}$.

Hence, the correct answer is option (A)