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 |
\[=\text{Area}\,\,\text{of}\,\,\Delta OCD-\text{Area}\,\,\text{of}\,\,\Delta OAB\] |
\[=\frac{1}{2}\times 3\times 2-\frac{1}{2}\times 1\times 1\] |
\[=3-\frac{1}{2}=2\frac{1}{2}\,\,\text{sq}\,\,\text{units}\] |
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