SOLUTION: A rectangle playground with an area of 900 square feet has a width that is 1/4 of its length. Write and solve an equation USING SQUARE ROOTS to find the dimensions of the pl

Algebra ->  Rectangles -> SOLUTION: A rectangle playground with an area of 900 square feet has a width that is 1/4 of its length. Write and solve an equation USING SQUARE ROOTS to find the dimensions of the pl      Log On


   

Question 966210: A rectangle playground with an area of 900 square feet has a width that is 1/4 of its length.
Write and solve an equation USING SQUARE ROOTS to find the dimensions of the playground.

Length _______ Width _______
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
W= width of the playground in feet.
L= length of the playground in feet.
W%2AL=900= area of the playground in square feet.
The problem states that the width is 1/4 of the length,
which in formula is W=L%2F4 .
Since I do not like denominators, I change that into an equivalent equation:
W=L%2F4 ---> 4W=L .
Then, substituting into W%2AL=900 , we get
W%2A%284W%29=900 ---> 4W%5E2=900 ---> W%5E2=900%2F4 ---> W%5E2=225 ---> W=sqrt%28225%29 ---> highlight%28W=15%29 .
(The other solution for the equation would be W=-sqrt%28225%29=-15 , but we are looking for a length, which is a positive number, so w=-15 is not a solution to the problem).
Then, substituting the value found into L=4W , we get
L=4%2A15 ---> highlight%28L=60%29 .
highlight%28Length=60+ft%29 , highlight%28Width=15+ft%29 .