Question

What is the area enclosed by the curve 2|x|+3|y| = 12.​

Answer 1

Answer:

The area enclosed by

is (a)3 sq. units (b) 4 sq. units (c)12 sq. units (d) 24 sq. units

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Answer 2

Answer:

$48 cm^{2}$ is the required area enclosed by the curve

Step-by-step explanation:

Explanation :

Given , 2| x | + 3| y | = 12

Here we can write the given equation in four different equation

such as, 2x +3y = 12 , -2x+3y = 12, -2x-3y = 12 and 2x-3y =12 .

These are the  four equation we have .

Step1:

For equation 2x + 3y = 12

put x = 0 , then y = 4 and when we put y = 0 than x = 6

For equation -2x + 3y = 12

put x = 0 then we get, y =4 and when y = 0 then x= -6

For equation -2x -3y = 12

put x = 0 then we get, y = -4 and when y = 0 then x= -6

For equation 2x - 3y = 12

put x = 0 then we get, y =-4 and when y = 0 then x =  6

Step 2:

When we plot all these points on the graph we get a parallelogram.

But we know that  area of a parallelogram = $\frac{1}{2} D_{1} .D_{2}$

Where $D_{1} ,D_{2}$ are the diagonal of the parallelogram .

From the graph we get ,

Length of $D_{1}$ = 12 cm  and  length of $D_{2}$ = 8cm

Now put the value of $D_{1} and D_{2}$ in the formula of parallelogram  we get ,

Area of a parallelogram = $\frac{1}{2} D_{1} .D_{2}$

                                          = $\frac{1}{2} .(12) .(8) = 48 cm^{2}$

Final answer :

Hence , area enclosed by the curve is $48cm^{2}$

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