SOLUTION: Find the area of a triangle bounded by the y-axis, the line f(x) = 7− (2)/(7)x and the line perpendicular to f(x) that passes through the origin. (Round your answer to two dec

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Find the area of a triangle bounded by the y-axis, the line f(x) = 7− (2)/(7)x and the line perpendicular to f(x) that passes through the origin. (Round your answer to two dec      Log On


   

Question 1174149: Find the area of a triangle bounded by the y-axis, the line
f(x) = 7− (2)/(7)x
and the line perpendicular to f(x) that passes through the origin. (Round your answer to two decimal places.)
Found 3 solutions by greenestamps, ewatrrr, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The three boundary lines are the y-axis, y = (-2/7)x+7, and y = (7/2)x.

The area of a triangle is one-half base times height.

Use the side of the triangle on the y-axis (length 7) as the base; then the height is the x value where the other two boundary lines intersect. So

(1) solve %287%2F2%29x+=+%28-2%2F7%29x%2B7 for x
(2) the area of the triangle is (1/2) times (7) times the value of x from step (1)

------------------------------------------

to the student....

The solution to %287%2F2%29x+=+%28-2%2F7%29x%2B7 is not x=1....

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 
Hi,
Find the area of a triangle bounded by the y-axis, the line f(x) = 7− (2)/(7)x
 y = -(2/7)x + 7
and the line perpendicular to f(x) that passes through the origin...
  y = (7/2)x
----------
    7 − (2/7)x = (7/2)x
    7 = (4 + 49)/14)x = (x)53/14
    (14/53)7 = x = 1.849  and y = 6.47   %287%2F2%29%281.849%29
-------------    
    D = +sqrt+%28+%28x%5B1%5D-x%5B2%5D%29%5E2%2B+%28y%5B1%5D-y%5B2%5D%29%5E2+%29+ 
    P(1.849, 6.47) &  P(0,0)    and      P(1.849, 6.47)  & P(0,7)

  Area = (1/2)bh = 



Will leave it to You to finish up.  Important You are comfortable with Your calculator.

Wish You the Best in your Studies.


Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.

            The solution by @ewatrrr looks frighteningly.

            It is because she selected  IMPROPER  way to solve the problem.

            Actually,  there is  MUCH  SIMPLER  way,  pointed by @greenestamps.

            I decided to complete the solution in that way to convince you  HOW  SIMPLE  it is. 


The two lines are


    y = %28-2%2F7%29x + 7

    y = %287%2F2%29x.


Their intersection is


    %28-2%2F7%29x+%2B+7 = %287%2F2%29x.


Multiply both sides by 14 to get


    -4x + 98 = 49x

          98 = 49x + 4x = 53x

           x            = 98%2F53.


You may consider the segment  [0,7]  along the y-axis as the base of our right-angled triangle.


Thus the base has the length of 7 units, while the altitude of the triangle, drawn to this base is  98%2F53  units long.


Hence, the area of the triangle is  %281%2F2%29%2A7%2A%2898%2F53%29 = 686%2F106 = 6.472  square units  (rounded).    ANSWER

Solved.

May the Lord saves you from solving the problem in a way how  @ewatrrr does it . . .

Let her post be a lesson for you on how this problem  SHOULD  NOT  be solved.