SOLUTION: In a rectangle co-ordinate system with a scale of 1 cm= 1 unit on each axis, we have A (0,8), B (6,0) and C (x,12). If x is larger than 0 but smaller than 6 and the area of ABC is

Algebra ->  College  -> Linear Algebra -> SOLUTION: In a rectangle co-ordinate system with a scale of 1 cm= 1 unit on each axis, we have A (0,8), B (6,0) and C (x,12). If x is larger than 0 but smaller than 6 and the area of ABC is       Log On


   

Question 1100997: In a rectangle co-ordinate system with a scale of 1 cm= 1 unit on each axis, we have A (0,8), B (6,0) and C (x,12). If x is larger than 0 but smaller than 6 and the area of ABC is 20cm^2, find the value of x.
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!

Add points D(0,12) and E(6,12) to the diagram, and call the origin point O.

The area of triangle ABC is the area of rectangle OBED, minus the areas of the three right triangles AOB, BEC, and CDA.

The area of rectangle OBED is 6*12 = 72.
The area of triangle AOB is 6*8/2 = 24.
The area of triangle BEC is 12(6-x)/2 = 36-6x.
The area of triangle CDA is 4*x/2 = 2x.

The area of triangle ABC is 72+-+24+-+%2836-6x%29+-+2x+=+12%2B4x
Since the area is supposed to be 20,
12%2B4x+=+20
4x+=+8
x+=+2