Question

zahar is planning to construct a fence for his garden and wants to estimate the total cost for the fencing. he represents his garden in a coordinate plane in which each unit represents 2 feet. the cost of fencing is $7.79 per foot. find the perimeter of the garden and the total cost of fencing. for help, see this worked example. type the correct answer in each box. use numerals instead of words. the perimeter is \boxed{} feet.

Explanation:

Step1: Identificar coordenadas de los vértices

Coordenadas: $A(0,1)$, $B(12,6)$, $C(12,11)$, $D(9,11)$, $E(0,5)$

Step2: Calcular longitud de cada lado

• $AB$: $\sqrt{(12-0)^2+(6-1)^2}=\sqrt{144+25}=\sqrt{169}=13$ unidades
• $BC$: $|11-6|=5$ unidades
• $CD$: $|12-9|=3$ unidades
• $DE$: $\sqrt{(0-9)^2+(5-11)^2}=\sqrt{81+36}=\sqrt{117}=3\sqrt{13}\approx10.8167$ unidades
• $EA$: $|5-1|=4$ unidades

Step3: Sumar longitudes (perímetro en unidades)

$13 + 5 + 3 + 10.8167 + 4 = 35.8167$ unidades

Step4: Convertir a pies (1 unidad = 2 pies)

$35.8167 \times 2 = 71.6334$ pies

Step5: Calcular costo total

$71.6334 \times 7.79 \approx 558.02$

Answer:

The perimeter is 71.63 feet.
The total cost is $\$558.02$