Question

Q1) draw the graph of 5x+6y-30=0 and use it to find the area of the triangle formed by the line and the coordinate axes.


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Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO DETERMINE

• To Draw the graph of 5x+6y-30=0

• Use it to find the area of the triangle formed by the line and the coordinate axes

CALCULATION

The given equation of the line is

$\sf{5x + 6y - 30 = 0}$

This equation can be rewritten as

$\sf{5x + 6y = 30}$

$\implies \: \displaystyle \sf{ \frac{5x}{30} + \frac{6y}{30} = 1}$

$\implies \: \displaystyle \sf{ \frac{x}{6} + \frac{y}{5} = 1}$

Which is of the intercept form

So the line cuts x axis at A ( 6, 0 ) and y axis B ( 0, 5)

Thus the triangle formed by the line and the coordinate axes is a Right angled triangle.

GRAPH : The graph is referred to the attachment

DETERMINATION OF AREA

The triangle is OAB with sides

OA = 6 unit , OB = 5 unit

Hence the required area of the triangle

$= \displaystyle \sf{ \frac{1}{2} \times 6 \times 5\: } \: \: \: sq \: unit$

$= \displaystyle \sf{ 15 } \: \: \: sq \: unit$

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