What is the area of the triangle?
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
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
a c
Favorite Answer
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.
Cheryl B
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=â20=2â5
Find the length of the other leg using the distance formula:
(4-0)²+(0-8)²=d²
16+64=d²
80=d²
d=4â5
Area = 1/2*(2â5+4â5)
=1/2*(6â5)
=3â5
_/
hayharbr
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.