SOLUTION: The area of a rectangular piece of concrete is 120 square feet, and its perimeter is 46 feet. What are the dimensions of the rectangle?

Question 6219: The area of a rectangular piece of concrete is 120 square feet, and its perimeter is 46 feet. What are the dimensions of the rectangle?
Found 2 solutions by minerva, arunpaul:
Answer by minerva(22) (Show Source): You can put this solution on YOUR website!
well,this is an easy one but requres concentration.

heres my solution.
statements:-
2(l+b)=46 (perimeter)
(l+b)=46/2
l+b=23
therfore l=23-b
SUBSTITTUTING THE VALUES:-
area=l X b=12
bX (23-b)=120
23b -b^2=120
-(b^2 -23b +120)=0
minus gets cancelled when diuvide d by 0
so, b^2 -23b +120=0
b^2 -15b-8b+120=0
b(b-15)-8(b-15)=0
b = 15 or b=8
then.... l=23-b
(a) 23-15=8 or (b)23-8=15
solution b is correct as length is always grteater than breadth

Answer by arunpaul(104) (Show Source): You can put this solution on YOUR website!
Let the length be = L
breadth be = B
as per the question
B*L =120 Sf eq1
perimeter = 2(L+B) = 46 ft eq2
again B = 120/L
put the value of B in eq2 we have
2L+(2*(120/L))=46
or 2L+(240/L)=46
or 2L^2+240 = 46L
or L^2+120 = 23L
or L^2+120 -23L=0
applying the solution of quadratic equation we have
a=1
b=120
c=-23
then applying the solution for quadratic equation we have

so L = 0.19136150644875 or -120.191361506449
take the positive value of L we have B= 120/0.19136150644875 =627.28
this seems some thing wrong in question though the solution is here

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