A farmer is building two rectangular pens for his animals, one for chickens and one for pigs. He plans to have them share a side. Using his measuring stick of length L feet, he measures the sides of the fence. The shared side is to be 5 feet longer than his stick, the second side of the chicken pen is to be 2 feet shorter than his stick, and the second side of the pig pen is to be the length of his stick. Write an expression for the sum of the areas of the two pens in fully factored form.
#Algebra
feral thunder
pure narwhalBOT
feral thunder
can somebody please help me
pale hare
start with the chichken pen
chicken*
you are given that "L" is the length of the stick
the shared side is 5 feet longer than the stick
so we will write L+5
the second side of the chicken pen is 2 feet shorter than the stick
so L-2
The area of the chicken pen would be (L+5)(L-2)
(L+5)(L-2)=L^2-2l+5L-10
L^2 + 3L - 10 is the area of the chicken pen
and for the area of the pig pen, the shared side is L-5 and the second side is just the length of the stick so it would just be L
so the area of the pig pen would be L(L+5)
L^2+5L is the area of the pig pen
so since the question is asking to write the sum of the areas of two pens
it would be the area of the chicken pen + area of the pig pen
so L^2+3L-10+L^2+5L
2L^2+8L-10
so we can factor out a 2
which will be
2(L^2+4L-5)
and so factor out L^2+4L-5
which is (L+5)(L-1)
so the answer should be 2(L+5)(L-1)
I hope that helps @feral thunder
polar anvil
pale hare
.solved