Question

❐Moderators
❐Brainly Stars
❐Other best users


Draw the graph representing the equations x - y = 1 and 2x + 3y = 12 on the same

graph paper. Find the area of the triangles formed by these lines, the X-axis and

the Y-axis​


Don't dare for spam !​

Answer 1

Given : Equation (1) is x - y = 1 and Equation (2) is 2x + 3y = 12.

To Find : Find the area of the triangles ?

_______________

Solution : Let the area of the triangles be x sq. units.

$~$

• ${\bf{\pmb{x~-~y~=~1}~~~~~~~~~~~~~~~~~~~~\bigg\lgroup{1}\bigg\rgroup}}$

$\qquad{\sf:\implies{x~=~y}}$

$~$

• Considering some points for plotting.

$~$

We get,

• If x = 0 , y = 0
• If x = 1 , y = 1
• If x = 3 , y = 3

$~$

Therefore,

• The required points for plotting,
• Eqⁿ (1) ; line are,

$\qquad:\implies{\underline{\boxed{\frak{\purple{\pmb{(0,0)~,~(1,1)~and~(3,3)}}}}}}$★

$~$

• ${\bf{\pmb{2x~+~3y ~=~12}~~~~~~~~~~~~~\bigg\lgroup{2}\bigg\rgroup}}$

$\qquad{\sf:\implies{2x~=~12~-~3y}}$

$\qquad{\sf:\implies{x~=~\dfrac{(12~-~3)}{2}}}$

$~$

• Finding the required points for plotting,

$~$

We get,

• If y = 0 , then x is :

$\qquad{\sf:\implies{x~=~\dfrac{(\cancel{12}~-~0)}{\cancel{2}}~=~\underline{\pmb{6}}}}$

• If y = 1 , then x is :

$\qquad{\sf:\implies{x~=~\dfrac{(12~-~3[1])}{2}}}$

$\qquad{\sf:\implies{x~=~\dfrac{(12~-~3)}{2}~=~\underline{\pmb{4.5}}}}$

• If y = 4 , then x is :

$\qquad{\sf:\implies{x~=~\dfrac{(12~-~3[4])}{2}}}$

$\qquad{\sf:\implies{x~=~\dfrac{(\cancel{12}~-~\cancel{12})}{2}}}$

$\qquad{\sf:\implies{\dfrac{x~=~0}{2~=~0}}}$

$~$

Therefore,

• The required points for plotting,
• Eqⁿ (2) ; line are,

$\qquad:\implies{\underline{\boxed{\frak{\purple{\pmb{(6,0)~,~(4.5,1)~and~(0,4)}}}}}}$★

$~$

• [Required to the attachment for the graph.]

$~$

Now, we are required to find the area of the triangle. (Yellow Part)

$~$

$\dag~\underline{\frak{\pmb{As ~we ~know ~that,}}}$

• $\boxed{\frak{\pmb{Area~of~ triangle~=~0.5~×~Base~×~Height}}}$

$~$

From, the diagram we can see that the top vertex is having a coordinate (2.4 , 2.4). Therefore, the distance of top vertex from x-axis is 2.4 units, Which is the height of the triangle.

• Similarly, the base of the triangle is from (0,0) to (6,0). Hence, the base length is 6 units.

$~$

Therefore,

$\qquad{\sf:\implies{Area~of~triangle~=~0.5~×~6~×~2.4}}$

$\qquad:\implies{\underline{\boxed{\frak{\pink{\pmb{7.2~sq.~units.}}}}}}$★

$~$

Hence,

• The area of the triangle is 7.2 sq. units.