Alg3.2.16

From Exampleproblems

Jump to: navigation, search

A farmer wishes to grow a 100 square meters rectangular vegetable garden.Since he has with him only 30meter barbed wire,he fences three sides of the rectangular garden letting compound wall of his house act as the fourth side-fence.Find the dimensions of the garden.

Let the length of one side is $x\,$ meters.

The other side will be $(30-2x)\,$ meters.

The are of the garden is $x(30-2x)\,$ square meters.

Given that $x(30-2x)=100,30x-2x^2=100,2x^2-30x+100=0\,$

$2x^2-20x-10x+100=0,2x(x-10)-10(x-10)=0,(2x-10)(x-10)=0\,$

$x=5,x=10\,$

If the length of the side is $5\,$ the other side is $30-2(5)=20\,$

If the length is $10\,$ meters, the other side is $30-2(10)=10\,$

The second one is not acceptable because the two sides are equal,which is a square,where as the given is a ractangular garden.

Therefore,the sides of the garden are $5,20\,$

Main Page:Algebra

Retrieved from "http://www.exampleproblems.com/wiki/index.php/Alg3.2.16"

Views

Personal tools

Create an account or log in

Search

Toolbox

Argan Oil
Natural Skin Care
Organic Skin Care