Question

Vanessa built a rectangular pen for her dogs. she used an outside wall of the garage for one side of the pen. she used 20 m of fencing in order to build the other 3 sides to complete the rectangle. find the dimensions of the pen of the pen if the area of the resulting pen was 48 m^2

Can you draw out the picture and help me find the two ( )( ) please

Answer 1

the 20m fencing is the perimeter I assume

Answer 2

2L+2W=20

Answer 3

then if the area is 48 its LW=48

Answer 4

length x width = 48
length + 2 width = 20

Answer 5

Oh ok I gotcha

Answer 6

8 + 2(6) = 20
8 + 12 = 20

8 * 6 = 48

Answer 7

Are you doing guess and check?

Answer 8

I didn't really use algebraic manipulation as I should have. it just came to me intuitively

Answer 9

I am making a few assumptions
one is that the opening of the fence is on the length side instead of the width side

Answer 10

I'm doing quadratics

Answer 11

Let one side be x
the other side = 48/x
2x+48/x =20
2x^2+48=20x
2x^2-20x+48=0

Answer 12

x^2-10x+24=0
x^2-6x-4x+24=0
x(x-6)-4(x-6)=0
(x-6)(x-4)=0
x=6 or 4 x=6 since we do not know whcich side of the garage was used
the dimensions of the pen could be 6m & 8m or 4 m & 12 m

Answer 13

I see

Answer 14

Or you could just isolate the l or w from L+2W=20
and plug that in with LW=48

Answer 15

Then get an equation, plug it into calculator, then get your x intercepts, whichever one works is ur answer..

Answer 16

like I said earlier that in my first attempt, I've made an assumption that the opening of the fence is on the length side
but the actual algebraic manipulation is more beautiful at actually obtaining the answer