SOLUTION: {{{drawing( 300, 300, -4, 6, -4, 6, locate( -2, 3, 200 ), locate( 1, -.5, 300 ), line(0,0,0,5), line(0,5,5,0), line(5,0,0,0) )}}} The diagram shows the dime

Algebra ->  Algebra  -> Surface-area -> SOLUTION: {{{drawing( 300, 300, -4, 6, -4, 6, locate( -2, 3, 200 ), locate( 1, -.5, 300 ), line(0,0,0,5), line(0,5,5,0), line(5,0,0,0) )}}} The diagram shows the dime      Log On

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Question 86090: drawing%28+300%2C+300%2C+-4%2C+6%2C+-4%2C+6%2C%0D%0A++locate%28+-2%2C+3%2C+200+%29%2C+%0D%0A++locate%28+1%2C+-.5%2C+300+%29%2C+%0D%0A++line%280%2C0%2C0%2C5%29%2C%0D%0A++line%280%2C5%2C5%2C0%29%2C%0D%0A++line%285%2C0%2C0%2C0%29%0D%0A+%29

The diagram shows the dimensions of a triangular field next to a
school. To estimate the number of wildflowers growing in the field,
students counted a total of 36 flowers in a randomly selected
3-feet-by-4-feet rectangular section. Assuming the section is a
representative sample of the entire field, approximately how many
flowers are in the entire field?

Answer by jim_thompson5910(14896) About Me  (Show Source):
You can put this solution on YOUR website!
First lets find the area of the triangle

The area of a triangle can be found by this formula:

Area=%28base%2Aheight%29%2F2

So if we have this trangle

drawing%28+500%2C+500%2C+-4%2C+6%2C+-4%2C+6%2C%0D%0A++locate%28+-2%2C+3%2C+height=200+%29%2C+%0D%0A++locate%28+1%2C+-.5%2C+base=300+%29%2C+%0D%0A++line%280%2C0%2C0%2C5%29%2C%0D%0A++line%280%2C5%2C5%2C0%29%2C%0D%0A++line%285%2C0%2C0%2C0%29%0D%0A+%29

We can clearly see that the base is 300 feet and the height is 200 feet
Now to find the area of this triangle, plug in base=300, height=200

Area=%28300%2A200%29%2F2

Area=%2860000%29%2F2 Multiply 300 and 200 to get 60,000

Area=30000 Divide 60,000 by 2 to get 30,000

Now since there are an average of 36 flowers in a 3 by 4 foot patch (which is 12 square feet), we can find the rough estimate of how many flowers are in the whole patch. If there are 36 flowers for every 12 square feet, we can set up a proportion (or ratio) to find the number of flowers there are for 30,000 square feet


36%2F12=x%2F30000 Start with the proportion where x is the number of flowers in a 30,000 square foot area

30000%2836%2F12%29=cross%2830000%29%28x%2Fcross%2830000%29%29 Multiply both sides by 30,000


30000%2A36%2F12=x Multiply

1080000%2F12=x Multiply

90000=x Divide

So x=90000

This means there are 90,000 flowers in the 30,000 square foot patch