Question

if the area of triangle formed by the points 5, 2 X - 5 and - 5, - 1 and 27 square units then find x

Answer 1

you should write properly. well, I observed you write " if the area of triangle formed by the points (5, 2) , (x, -5) and (-5, -1) is 27 square unit then find x ?

sol : area of triangle = $\frac{1}{2}|[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]|$

= 1/2|[5(-5 + 1) + x(-1 - 2) + (-5)(2 + 5)]

= 1/2|[5(-4) - 3x - 35 ]|

= 1/2 |[ -20 - 3x - 35]|

= 1/2 | - 55 - 3x |

hence, 27 = 1/2 |-55 - 3x|

or, 54 = |-55 - 3x|

or, ± 54 = -55 - 3x

or, -3x = ±54 + 55

3x = $\mp54-55$

x = -109/3 and -1/3