Question 102056This question is from textbook
: find te area of the triangular region enclosed by the y-axix and the graphs of 6x+5y=30 and 2x-y=2. This question is from textbook
You can put this solution on YOUR website! Ok well first lets graph the two lines and see what we have.
Now we can see that these lines do intersect with the y intercept and each other to form a triangle.
Ok so we want to find out what the area of this triangle is. First what is the formula for area of a triangle?
A= 1/2(b)(H)
Thats Area equals one half times base times height.
Now we have to figure out the base and height for our triangle.
Looking at the graph we can see that our triangle is actually turned on its side. So the base will be the side of the triangle that is shown by the y axis. Or in other words the base is the distance between the y intercept points for each of our lines.
The lines cross the y axis at 6 and -2. The distance between these points is 8 so the length of the base is 8.
Now we need to find the height. Remember the triangle is on its side so the highest point on the triangle is actually the intersection of the two lines we graphed. This intersection is at point (2.5,3) So the height is 2.5
Now we can finally use the formula for area of a triangle.
A = 1/2(8)(2.5)
A = 10
