SOLUTION: 1)A farmer wishes to grow a 100 m^2 rectangular vegetable garden.Since he has with him only 30 m barbed wire, he fences three sides of the rectangular garden letting compound wall

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Question 10269: 1)A farmer wishes to grow a 100 m^2 rectangular vegetable garden.Since he has with him only 30 m barbed wire, he fences three sides of the rectangular garden letting compound wall of his houseact as the fourth side-fence.Find the dimensions of his garden.
[Hint:If the length of one side is x metres, the other side will be (30-2x)m.Therefore,x(30-2x)=100]
Answer by rapaljer(4551) About Me  (Show Source):
You can put this solution on YOUR website!
Your set up is right. Just solve the equation, which is a quadratic equation. These types of equations nearly almost always factor. You are letting x = the length of each of the two equal sides, where the 30-x represents the side parallel to the house.

x(30-2x) = 100
30x+-+2x%5E2+=+100

Set the equation equal to zero, preferably with the x%5E2 term positive. To do this take everything to the right side, by adding 2x%5E2+-+30x+ to each side of the equation.
0+=+2x%5E2+-+30x+%2B+100

From this, you can factor out the common factor of 2.
0+=+2%28x%5E2+-+15x+%2B+50%29+

Now factor the trinomial:
0+=+2%28x-5%29%28x-10%29+

There are two solutions:
x=5, x=10

If x=5 m, the other side is 30-2x = 20 m.

If x = 10 m, the other side is 30-2x = 10 m.

Both solutions work in that the perimeter is 30 m, and the area is 100 m^2.

R^2 at SCC