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

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)   (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 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 is not x=1....

Answer by ewatrrr(24785)   (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 ------------- D = 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)   (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 = + 7 y = . Their intersection is = . Multiply both sides by 14 to get -4x + 98 = 49x 98 = 49x + 4x = 53x x = . 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 units long. Hence, the area of the triangle is = = 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.

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