Question
Thu January 27, 2011 By: Priyanka R

find

Expert Reply
Wed February 09, 2011

Dear Student,

Here is the solution:

Only lines with a negative slope will cut a triangle in the First Quadrant.
if you experiment with this idea, you should (hopefuly) see that the best line for a minimum area would have a slope of about negative one.
This is only the starting point for solving this problem.
Now you should calculate the area of a triangle generated in this way.

Equation Y = mX + b
m = slope of line
b = y intercept
And remember to use the point on the line. So Y = 4 when X = 3.

Example Triangle #1:
Let m = -1

Y = mX + b
4 = (-1)(3) + b
4 = -3 + b
b = 7
#1 Equation is Y = -1X + 7

Draw this on a Graph to see the triangle!
Now calculate its Area.
The length along the y axis is 7.
The length along the x axis is X when Y = 0.
0 = -1X + 7
X = 7
Area = 0.5 ( 7 )( 7 ) = 24.5 square units.


You can continue to change the slope or the y intercept and recalculate the area.
I calculated an Area = 0.5 ( -b / m )( b ) = -3 b^2 / ( 8 - 2b )
min. Area = 24 square units {{{ close to the 24.5 earlier }}}
Then found a slope of -4/3.
And a y intercept of 8.

The final equation came out as Y = (-4/3) X + 8

 

Reagrds

Team Topperlearning.

Wed September 27, 2017

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