Triangle geometry

Question

The sides of a triangle are formed by parts of the lines y+3x=11, 3y=X+3 and 7y+X=37

 

1)Find the coordinates of the vertices of the triangle. 

 

2)Show that the triangle is right angled. 

 

3)work our the area of the triangle. 

Answer 1

(2,5), (3,2), (9.4)

hypotenuse = sqr50

sides are sqr40 and sqr10

sum of squares of sides = square of hypotenuse

40+10 = 50

Area = half multiple of sides = (1/2)sqr10sqr40 = 1/2sqr50 = 5/2sqr2 = about 5/2(1.4) = 3.4