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  • The sides of a rectangle are , and <img alt="\mathrm{y=3}" src="

The sides of a rectangle are \mathrm{x=0, y=0, x=4}, and \mathrm{y=3}. The equation of straight line having slope \mathrm{\frac{1}{2}} that divides the rectangle in to two equal halves is

Option: 1

\mathrm{2 y=x+1}


Option: 2

\mathrm{2 x=y+1}


Option: 3

\mathrm{2 y+x=1}


Option: 4

\mathrm{2 x+y=1}


Answers (1)

best_answer

Let the required line be \mathrm{2 y=x+c}.

We have

\mathrm{A_{1}\left(4, \frac{4+C}{2}\right), B_{1}\left(0, \frac{c}{2}\right)} Area of rectangle \mathrm{A B C D} is 12 sq. units
Thus area of trapezium \mathrm{O A A_{1} B} is


\mathrm{6=\frac{1}{2}(4)\left(\frac{c}{2}+\frac{4+C}{2}\right) \Rightarrow c=1}

Thus required line is \mathrm{2 y=x+1}

Hence (A) is the correct answer.

Posted by

jitender.kumar

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