Question

If the area of the triangle formed by the straight lines x = 0, y = 0, 3x + 4y = a is 6. Then find the value of 'a'

Answer 1

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Answer 2

The value of a is 12.

Given,

The area of the triangle formed by the straight lines x = 0, y = 0, 3x + 4y = a is 6.

To FInd,

The value of a.

Solution,

The given three lines are x = 0, y = 0, and 3x + 4y = a.

The height and the base of the triangle will be the points where the line 3x+4y = a meets the axes because x = 0 and y = 0 is the equation of coordinate axes.

So, putting y = 0 in the equation of line

3x+4(0) = a

x = a/3

Now,

3(0)+4y = a

y = a/4

So, the height and base of the triangle will be a/3 and a/4.

Now,

Area of triangle = 6

1/2(a/3)(a/4) = 6

a² = 144

a = 12

Hence, the value of a is 12.

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