Question

4. A farm decided to construct a portion of his area close to his house for chicken farming.

He decided to fence a rectangular area of length 4x and width of 1.5x², the length is

measured with uncertainty of 12 cm and width of 24 cm uncertainty. If the maximum

perimeter of this area is 350 m.

a) Find the length and width.

b) Calculate the area of this portion of land.

c) Calculate the percentage of uncertainty of the minimum area.

Answer 1

a)

$$2(1.5x^2+4x)=350\to x=9.55$$

$$w=1.5(9.55)^2=136.80\ m\\l=4(9.55)=38.20\ m$$

b)

$$A=136.80\cdot 38.20=5225.76\ m^2$$

c)

$$\epsilon=\frac{0.12}{38.20}100\%+\frac{0.24}{136.80}100\%=0.49\%$$