Question

find the area of triangle if triangle made by x axis and y axis and linear equation 15x + 12y = 27​

Answer 1

Answer: 2.025 sq units.

Explanation:

X intercept: (9/5, 0).

As, 15x - 12(0) = 27

[X - axis equation : y = 0.]

=> 15x = 27

=> x = 27/15 = 9/5 = 1.8 units

Y intercept: (0, 9/4).

Since, 15(0) + 12y = 27

[Y - axis = x = 0.]

=> 12y = 27

=> y = 27/12 = 9/4 = 2.25

Now, area of ∆ = 1/2 bh = 1/2(ordinate)(abscissa)

=> ∆ = 1/2(1.8)(2.25) = 2.025 sq units.

Four new methods:

• Use can also use:

$\rm \Delta = \dfrac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) |$.

(As coordinates are known.)

• Plot the solutions on a graph paper and record where it meets the axes. Now find the area.
• Use: $\rm \dfrac{1}{2} ab \sin C$.
• Further you can also use the Heron's formula:

$\rm \sqrt{s(s - a)(s - b)(s - c)}$.