What is the area of the triangle?

Question

use the following information to answer the above question. The equations below represent two lines that intersect the y - axis to form a triangle. 2x + y = 8 and x - 2y = 4

Answer 1

First, let's put the lines in slope-intercept form:

2x+y=8

y=-2x+8

x-2y=4

-2y=-x+4

y=(1/2)x-2

From this we learn two things.  First, the two y-intercepts are +8 and -2, which gives us the points (0,8) and (0,-2). Second, because the slopes are negative reciprocals, the lines are perpendicular.  This is good, because to find the area of a right triangle, you just take 1/2 * leg * leg

To find the third point, set the two equations equal to each other and see where the intersect:

-2x+8=(1/2)x-2

-4x+16=x-4

16=5x-4

20=5x

x=4

When x=4, solve for y:

2x+y=8

2*4+y=8

8+y=8

y=0.

So the third point is (4,0)

Find the length of one leg by using the distance formula:

(4-0)² + (0+2)²=d²

16+4=d²

d=√20=2√5

Find the length of the other leg using the distance formula:

(4-0)²+(0-8)²=d²

16+64=d²

80=d²

d=4√5

Area = 1/2*(2√5+4√5)

=1/2*(6√5)

=3√5

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Answer 2

When you draw each line, you see that they intersect on the x-axis at the point (4,0).  You also see that they hit the y axis at 8 and -2.  If you turn your graph sideways you see that the triangle has a base of 10 and a height of 4 so its area is 1/2 (10)4 , 1/2 of 40 which is 20.

Answer 3

sadly the last poster got the last step wrong

area = b*h/2

Area = 1/2*(2√5*4√5)

=1/2*(8*5)

=1/2*40

=20units squared.