question_answer

The area (in sq units) bounded by the lines \[x=0,\]\[y=0,\]\[x+y=1\]and \[2x+3y=6\]is [SSC (CGL) 2012]

A) 2                                 

B) \[2\frac{1}{3}\]

C) \[2\frac{1}{2}\] 

D) 3

Correct Answer: C

Solution :

Given tines are

\[x=0\]                                      ... (i)

\[y=0\]                                      ... (ii)

\[x+y=1\]                                 ... (iii)

\[2x+3y=6\]                              ... (iv)

\[x=0\]is the equation of Y-axis.

\[y=0\]is the equation of X-axis.

On putting \[x=0\]in Eq. (iii), we get \[y=1\]

On putting \[y=0\] in Eq. (iii), we get \[x=1\]

On putting\[x=0\] in Eq. (iv), we get

\[3y=6\]\[\Rightarrow \]\[y=2\]

On putting \[y=0\]in Eq. (iv), we get

\[2x=6\]\[\Rightarrow \]\[x=3\]

\[\therefore \]      \[OB=1\]

\[\Rightarrow \]   \[OA=1\]\[\Rightarrow \]\[OD=3\]

and       \[OC=2\]

\[\therefore \]Required area

\[=\text{Area}\,\,\text{of}\,\,\Delta OCD-\text{Area}\,\,\text{of}\,\,\Delta OAB\]

\[=\frac{1}{2}\times 3\times 2-\frac{1}{2}\times 1\times 1\]

\[=3-\frac{1}{2}=2\frac{1}{2}\,\,\text{sq}\,\,\text{units}\]