SOLUTION: the area of square field is 5184 m. square. a rectangular field , whose length is twice its breadth has its perimeter equal to the perimeter of the square field . find the area of

Algebra ->  Exponents -> SOLUTION: the area of square field is 5184 m. square. a rectangular field , whose length is twice its breadth has its perimeter equal to the perimeter of the square field . find the area of       Log On


   

Question 99525: the area of square field is 5184 m. square. a rectangular field , whose length is twice its breadth has its perimeter equal to the perimeter of the square field . find the area of the rectangular field.
Answer by doukungfoo(195) About Me  (Show Source):
You can put this solution on YOUR website!
First lets look at the square field. We are given that its area equals 5184 m.
Lets find its perimeter. We know that the area of a square is equal to its length times its width. or %28L%29%28W%29=5184 because it is a square we know that its length and width are equal so to find them all we have to do is take the square root of 5184. so sqrt%285184%29=72
Now we know that each side of the square field is 72 meters.
The perimeter of a square is equal to the sum of all its sides.
Since there are four sides to a square, all we have to do to find the perimeter is multiply 4 times 72. Ok well %284%29%2872%29=288
So the perimeter of the square field is 288 meters.
Now lets take a look at the rectangle field.
Lets use L and W to describe its length (L) and its width (W)
We are told that its length is twice its breadth (or width)
lets write that as an equation
L=2W
Thats length equals two times width.
We are also told that its perimeter is equal to the perimeter of the square field. And we know that the square field perimeter is 288 meters.
The perimeter of a rectangle is equal to the sum of all its sides.
since there are two sides that represent the length and two sides that represent the width we can express the perimeter of the rectangle field with this equation:
%282L%29%2B%282W%29=288
Now because we are told that L=2W
we can replace the L in %282L%29%2B%282W%29=72 with 2W like this:
%282%282W%29%29%2B%282W%29=288
Now we can solve for W
%282%282W%29%29%2B%282W%29=288
%284W%29%2B%282W%29=288
6W=288
W=48
Ok so the width of the rectangle field is 48 meters.
We can now use this to find the length.
%282L%29%2B%282W%29=288
%282L%29%2B%282%2848%29%29=288
%282L%29%2B%2896%29=288
%282L%29=288-96
%282L%29=192
L=96
Finally we have found the length of the rectangle field to be 96 meters
and the width to be 48 meters. To find the area of this field all that is left
to do is multiply its length (96) times is width (48) so
%2896%29%2848%29=4608+m%5E2