Question 1012550
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Find vertices
Intersection of 5x+7y=35 (red on graph) and x-axis (purple on graph):
Set y=0, solve for x
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5x+7(0)=35
5x=35
x=7
One vertex is (7,0)(red crosses purple)
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Intersection of 4x+3y=12 (green on graph) and x axis (purple on graph):
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4x+3(0)=12
4x=12
x=3
Second vertex at (3,0) (green crosses purple)
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The base is from (3,0)to (7,0)
Length of base is (7-3)=4
b=4
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5x+7y=35 . Multiply this by 3 (red on graph)
4x+3y=12 . Multiply this by 7 (green on graph)
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15x+21y=105
28x+21y=84 . Subtract second from first
-13x=21
x=-21/13
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5x+7y=35
5(-21/13)+7y=35
-105/13+7y=35
7y=455/13+105/13
7y=560/13
y=80/13
Third vertex is (-21/13,80/13) (red crosses green)
The height of the triangle is the y-value of this vertex.
h=80/13
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{{{Area=(1/2)bh}}}
{{{Area=(1/2)(4)(80/13)}}}
{{{Area=160/13}}} square units
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{{{ graph( 800, 800, -10, 10, -10, 10, (-5/7)x+5, (-4/3)x+4, y=0) }}}