SOLUTION: Is it possible to have a rectangular playground area made from 70 yards of fencing with an area of 324 square yards? Explain with calculations.

Question 949978: Is it possible to have a rectangular playground area made from 70 yards of fencing with an area of 324 square yards? Explain with calculations.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Perimeter(P) = 2*length(l) + 2*width(w) and
Area(A) = l*w
we are given
2*l +2*w = 70 and
l*w = 324
solve first equation for l and subsitute in second equation for l
2l = 70 -2w
l = 35 -w
2*(35-w) *w = 324
(70-2w)*w = 324
-2w^2 +70w -324 = 0
divide both sides of = by -2
w^2 -35w +162 = 0
using quadratic formula to solve we have
w = (35+24.020824299) / 2 = 29.510412149 is approx 29.5 yards
w = (35-24.020824299) / 2 = 5.489587851 is approx 5.5 yards
we have two cases, width is either 29.5 yards or 5.5 yards
*********
if width is 29.5, then
2*l + 2*29.5 = 70
2l + 59 = 70
2l = 11
l = 5.5 and
5.5 * 29.5 = 324
162.25 does not equal 324
**********
if width is 5.5, then length is 29.5 and
29.5 * 5.5 = 324
162.25 does not equal 324
**********
It is not possible to build this rectangular playground area

RELATED QUESTIONS
Is it possible to have a playground area made from 70 yards of fencing with an area of... (answered by Alan3354)

A city park commission received a donation of playground equipment from a parents'... (answered by josgarithmetic,ikleyn,greenestamps)

Suppose that the playground area has a length of x yards and a width of y yards. The only (answered by rothauserc,MathLover1)

A woman has 8 yards of fencing for her yard. What is the maximum rectangular area she can (answered by MathLover1)

I can't come up with an answer to this problem, i was thinking that it has to be more... (answered by Earlsdon)

A playground has an area of 225 yards squared. The number of yards on each side will be a (answered by josmiceli)

The community is planning to construct a rectangular playground within the local park.... (answered by josgarithmetic)

If a square region has an area of 90 square yards, what is the amount of fencing needed... (answered by katealdridge)

New playground will be rectangler and have an area of 225 yrds 2. The number of yards on... (answered by childress)