GATE ECE 2016 Set 3 | GA | Question: 9

Question

Find the area bounded by the lines $3x+2y=14$, $2x-3y=5$ in the first quadrant.

• A. $14.95$
• B. $15.25$
• C. $15.70$
• D. $20.35$

Comments

15.25 sq units

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Bt how it will come 15.25 square units can someone expkain plz

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solve for x and y, observe that two given lines are perpendicular. so it will form something like rectangle in first quadrant.

now coordinates of rectangle are (0,0) (x,0) (0,y) (x,y)

find area = length * breadth

Answer 1

• $3x+2y=14\rightarrow(1)$
• $2x−3y=5\rightarrow(2)$

To get the intersection point, we solve the equations and get $x=4,y=1$

We can draw the required area like this 

 

From the above diagram,

Area $=\triangle ABC +\Box OBCE-\triangle CDE$

Area $=\left(\dfrac{1}{2}\times 4\times 6\right)+\left(1\times 4\right)-\left(\dfrac{1}{2}\times\dfrac{3}{2}\times 1\right)$

Area $=12+4-\dfrac{3}{4}=16-0.75=15.25$

So, the correct answer is $(B).$

Comments

Yeah, In question they should mention which axis. B’coz if we take first lower part then upper part, this will be a time-consuming problem.

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In the figure why △ DFC area is not taken??

Question is :

Find the area bounded by the lines 3x+2y=14 , 2x−3y=5 in the first quadrant.

And this area alone satisfies all conditions bounded by two lines given and also in the first quadrant. Isn’t it ??

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@ASNR1010 @Deepak Poonia Sir @Lakshman Patel RJIT . In the question it is given that we need to find the area in first quadrant then why are we finding the area bounded by Y-axis ??

Answer 2

ans may be like this

Comments

Hello can the picture be more clear please?

Answer 3

I have one more simpler approach for you ,Consider the same diagram as @Lakshman Bhaiya  given below.

Now oberserve the diagram and figure out two things there is a triangle ABC and a trapezium BCDO

area of bounded region is :Area of ABC + area of trapezium BCDO:

1/2*B*H+ 1/2*(Sum  of paraller sides)*H

1/2*4*6+1/2*6.5*1=12+3.25=15.25
SO correct answer is (B)