SOLUTION: Dear Tutors, The question asks: The area of a rectangular playground is 2,700 ft2. The length is 3 times the width. What are the dimensions of the play ground? Please hel

Algebra ->  Surface-area -> SOLUTION: Dear Tutors, The question asks: The area of a rectangular playground is 2,700 ft2. The length is 3 times the width. What are the dimensions of the play ground? Please hel      Log On


   

Question 120072: Dear Tutors,
The question asks:


The area of a rectangular playground is 2,700 ft2. The length is 3 times the width. What are the dimensions of the play ground? Please help!!!THANKS
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
First we know that the area of a rectangle is given by A=lw, so we can write:

lw=2700

But we also know that the length, l, is three times the width w, so we can write:

l=3w

Now we can change the first equation to read:

3w%2Aw=2700, or 3w%5E2=2700

Divide both sides by 3

w%5E2=900

Take the square root of both sides:

sqrt%28w%5E2%29=sqrt%28900%29

w=30 or w=-30. However, since we are looking for a measure of length, we can exclude the w=-30 result.

Since we know that l=3w, we now know that l=3%2A30=90.

So the dimensions of the playground are 90 feet by 30 feet.

Check:
90%2A30=2700 and 3%2A30=90: Checks!

Hope that helps.
John