SOLUTION: the length of a rectangular field is 3 times its width. If the perimeter of the field is 24m,then area of the same is

Algebra ->  Length-and-distance -> SOLUTION: the length of a rectangular field is 3 times its width. If the perimeter of the field is 24m,then area of the same is      Log On


   

Question 753158: the length of a rectangular field is 3 times its width. If the perimeter of the field is 24m,then area of the same is
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
STARTINF NOYES:
Since the perimeter is measured in meters, we will measure length and width in meters, and we will calculate area in square meters.
There is usually more than one way to solve a problem. I'll show you some ways. Use the way to solve the problem that you think your teacher prefers, or the one the teacher thinks is the right way to do it. (Your teacher may not like to use the --> arrows that I use, for example).

DEFINING VARIABLES AT THE START:
w= width
Length = 3w
Perimeter = 2%28w%2B3w%29=2%284w%29=8w
Area = Length X Width or
Area = w%2A%283w%29=3w%5E2
{You could use x or anything else instead of w).

ONE WAY FROM THERE ON:
system%28Perimeter=8w%2CPerimeter=24%29 --> 8w=24 --> w=24%2F8 --> w=3
The width is 3 meters.
From here:
Length = 3 x 3 meters = 9 meters and
Area = Length X Width = (9 meters) X (3 meters) = highlight%2827%29 square meters

FANCIER:
After finding w=3,
system%28Area=3w%5E2%2Cw=3%29 --> Area=3%2A3%5E2 --> Area=3%2A9 --> highlight%28Area=27%29 (in square meters) or highlight%28Area=27m%5E2%29

TOO FANCY:
Perimeter=8w --> w=Perimeter%2F8
system%28Area=3w%5E2%2CPerimeter=8w%29 --> Area=3%28Perimeter%2F8%29%5E2 <--> Area=3Perimeter%5E2%2F8%5E2
So Area=3%2824%2F8%29%5E2 or Area=3%2A24%5E2%2F8%5E2
The easier calculation is
Area=3%2824%2F8%29%5E2 --> Area=3%283%29%5E2 --> Area=3%2A9 --> highlight%28Area=27%29 (in square meters) or highlight%28Area=27m%5E2%29