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SSC CGL 2022 PYQ — Question 33

SSC CGL Tier II - Quant - 29 Jan 2022 • Quantitative Aptitude • Q33

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What is the area (in unit squares) of the region enclosed by the graphs of the equations 2x - 3y + 6 = 0, 4x + y = 16, and y = 0?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 14.

For 2x - 3y = -6

x 0 -3
y 2 0

 

For 4x + y = 16

x 3 4
y 4 0

 

From the above figure the vertices of the triangle will be (3,4), (-3,0), and (4,0)

  Formula for the Area of triangle 12∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)∣⇒12∣3(0−0)+4(0−4)+(−3)(4−0)∣⇒12∣0+(−16)+(−12)∣⇒12∣−16−12∣⇒12∣−28∣ \begin{aligned} &\text { Formula for the Area of triangle }\\ &\frac{1}{2}\left|x_{1}\left(y_{2}-y_{3}\right)+x_{2}\left(y_{3}-y_{1}\right)+x_{3}\left(y_{1}-y_{2}\right)\right| \\ &\Rightarrow \frac{1}{2}|3(0-0)+4(0-4)+(-3)(4-0)| \\ &\Rightarrow \frac{1}{2}|0+(-16)+(-12)| \\ &\Rightarrow \frac{1}{2}|-16-12| \\ &\Rightarrow \frac{1}{2}|-28| \end{aligned}

= 14.