Word Problem

Question

Farmer Brown built a rectangular pen for his chickens using 16 meters of fence. He used part of one sire of his barn as one length of the rectangular pen. He maximized the area using the 16 meters of fence . Farmer Johnson built a rectangular pen for her chickens using 20 meters of fence. She used part of one side of her barn as one length of the rectangular pen. The length of her pen was 2 meters more than the length of Farmer Brown's pen. How much larger is Farmer Johnson's rectangular pen than Farmer Brown's?

I need the steps along with the answer please!

Answer 1

P=2l+2w

16=2l+2w

8=l+w

8-l=w

A=lw

A=l(8-l)

A=8l-l²

use -b/2a for the h value of the vertex of the parabola

 -b/2a=-8/-2=4 m for each side

because he used one side of the barn as part of the rectangle, put that 4 m with the opposite side to get 8 m

the rectangle is 4m by 8m by 4m by "the side of the barn"

A=lw

A=4*8=32 square meters

Farmer Johnson has 20 meters of fence. The length of her pen is 2 m more than the length of farmer Brown's length.

8+2=10m for the length and 5m for each width (she also used one side of the barn)

her rectangle is 5m by 10m by 5m by "the side of the barn."

A=lw=4*8=32 sq m

A=lw=5*10=50 sq m

50-32=18 sq m larger is farmer Johnson's pen