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Can some one explain this solution in detail

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Can some one explain this solution in detail [#permalink] New post 12 Jul 2004, 22:35
CAN SOME ONE EXPLAIN ME THIS SOLUTION :roll: :?: :!:


Find area if a line goes through x's greater than or equal 2, y's greater than or equal 3, and y's less than or equal to 9-x.

Please solve!

The area is that of a triangle with points (2,3) (2,7) (6,3)
height and base of triangle is 4 and represents a isoceles right triangle
area is 4*4/2 = 8


Paul
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 [#permalink] New post 13 Jul 2004, 23:53
Find area if a line goes through x's greater than or equal 2, y's greater than or equal 3, and y's less than or equal to 9-x.

Solution -

Plot the points .. (the key to this question is to find three points to make the triangle).

We know X is minimum 2
Y is minimum 3

so we get one point as (2,3) and Use these 2 co-ordinates (x=2 , y=3) in the equation y=9-x.

For x =2, Y=7
For y=3, x=6

Now we have 3 points to make a triangle. (2,3), (2,7) and (6,3). From this we know that the the lenghts of 2 sides are 4. This makes it isocls triangle. Are is bh/2. 4x4/2 = 8.

I hope this helped.
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Re: Can some one explain this solution in detail [#permalink] New post 14 Jul 2004, 06:57
K_s_r wrote:
CAN SOME ONE EXPLAIN ME THIS SOLUTION :roll: :?: :!:


Find area if a line goes through x's greater than or equal 2, y's greater than or equal 3, and y's less than or equal to 9-x.

Please solve!

The area is that of a triangle with points (2,3) (2,7) (6,3)
height and base of triangle is 4 and represents a isoceles right triangle
area is 4*4/2 = 8


Paul



There are 3 points of intersection for these 3 lines (X>=2, Y >= 3, Y <= 9-X), their coords were listed by Paul. Then we note that the triangle, formed by these 3 points is right and calculate its area by multiplying 2 sides which form right angle and dividing the result by 2.

4*4/2 = 8 is the answer.
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 [#permalink] New post 14 Jul 2004, 20:59
Thank you both of you. That was really helpful.

I just went on subsituting the X value and got Y values, never tried the other direction.
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 [#permalink] New post 16 Jul 2004, 14:28
I'm in trouble on this one.
picked 3 points accordingly:
(2,3), (3,6), (6,3)
from this, base of the triangle is equal to 4, and height is equal to 3
1/2*3*4=6, not 8!!

What am I doing wrong?
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 [#permalink] New post 16 Jul 2004, 21:57
lastochka wrote:
I'm in trouble on this one.
picked 3 points accordingly:
(2,3), (3,6), (6,3)
from this, base of the triangle is equal to 4, and height is equal to 3
1/2*3*4=6, not 8!!

What am I doing wrong?


I guess the problem is here

u took the numbers (2,3) and did not derive the next points from these two numbers, you just pulled out x = 3 and got the points (3,6) & (6,3)

That may not really satisfy the conditions

But I also have problem with the follwing poitns

take (x,y) = (3,4) then 2nd poitn becomes x,y = 3,6 & 3rd is x,y = 5,4

Hmmmmmmmm,

Good poitn some one explain,
  [#permalink] 16 Jul 2004, 21:57
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