SOLUTION: Mr.Jackson had a rectangular shaped garden where the length is less than twice the width. If the area of the garden is 420 sq. Ft, find the dimension of the garden?

Algebra ->  Rectangles -> SOLUTION: Mr.Jackson had a rectangular shaped garden where the length is less than twice the width. If the area of the garden is 420 sq. Ft, find the dimension of the garden?      Log On


   

Question 894142: Mr.Jackson had a rectangular shaped garden where the length is less than twice the width.
If the area of the garden is 420 sq. Ft, find the dimension of the garden?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The way described, this is an inequality problem.

w for width, L for length.

L%3C2w and wL=420. These are exact translations according to the description.

From area equation, L=420%2Fw.
Substituting into your inequality,
420%2Fw%3C2w
420%2Fw-2w%3C0
210%2Fw-w%3C0
210%2Fw-w%5E2%2Fw%3C0, because need common denominator;
%28210-w%5E2%29%3C0, because now we are not interested in the NUMERATOR being less than zero; the denominator is of no relevance for that.

210%3Cw%5E2
w%3Esqrt%28210%29
w%3Esqrt%283%2A7%2A2%2A5%29, prime numbers only occurring one time each; so just stick with the 210;
highlight%28w%3Esqrt%28210%29=14.4914%29

Now for finding L.
L<2w
highlight%28L%3C2sqrt%28210%29%29
OR
L%3C2%2A14.4914
highlight%28L%3C28.983%29


Note also, since you are finding rectangle dimensions, 0%3CL%3C28.983 and 14.4914%3Cw%3C28.983