Question 68245: Hi, could you please help me on how to solve this problem?
Determine the area of the triangle bounded by the following equations using Heron's formula: x-2y=12, x+3y=9, and 4x-y=-16. I know the Heron's formula but I do not know how to solve the problem. I first put the equations in function form but I don't know if that is how to solve the problem.
Please help me! I need this for homework that is due in three days!
Thank you.
Answer by adamchapman(301)   (Show Source):
You can put this solution on YOUR website! I have plotted the lines for you.
You can see where the 3 lines intercepet above.
These points can be found by simulataneously solving the 3 equations you worked out.
Let's do that now:
 ...(1)
 ...(2)
 ...(3)
rearrange equation (1) to give x in terms of y
 and put this new value for x into equation (2):
If we put this value for y into the expression we had for x, we get:
Following the process above similarly for equations (1) and (2), (2) and (3), finally (1) and (3) you will obtain the location of the three corners of the triangle in (x,y) coordinates.
Now find the lengths of the three sides by using:
where L is the length between the points (x1,y1) and (x2,y2). Do this for all three combinations of the 2 points you obtained earlier. Call these lengths a,b and c.
Now you have the lengths, you can calculate the 'semiperimeter', also called 's', using:
Now we can use Heron's formula to find the area:
I hope this has helped you. If you have any further questions, please email me or visit my website at www.geocities.com/quibowibbler .
Best Regards,
Adam
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